answers (lesson 1-1) - central dauphin school district · 2019-08-29 · chapter 1 a3 glencoe...
TRANSCRIPT
Chapter 1 A1 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-1)
STEP
1
Cha
pter
13
Gle
ncoe
Alg
ebra
2
NA
ME
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AT
E__
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ER
IOD
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1
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ant
icip
atio
n G
uide
Eq
uat
ion
s an
d In
equ
alit
ies
Chapter Resources
Bef
ore
you
beg
in C
ha
pte
r 1
•R
ead
each
sta
tem
ent.
•D
ecid
e w
het
her
you
Agr
ee (
A)
or D
isag
ree
(D)
wit
h t
he
stat
emen
t.
•W
rite
A o
r D
in
th
e fi
rst
colu
mn
OR
if
you
are
not
su
re w
het
her
you
agr
ee o
r di
sagr
ee,
wri
te N
S (
Not
Su
re).
Aft
er y
ou c
omp
lete
Ch
ap
ter
1
•R
erea
d ea
ch s
tate
men
t an
d co
mpl
ete
the
last
col
um
n b
y en
teri
ng
an A
or
a D
.
•D
id a
ny
of y
our
opin
ion
s ab
out
the
stat
emen
ts c
han
ge f
rom
th
e fi
rst
colu
mn
?
•F
or t
hos
e st
atem
ents
th
at y
ou m
ark
wit
h a
D,u
se a
pie
ce o
f pa
per
to w
rite
an
exa
mpl
e of
wh
y yo
u d
isag
ree.
ST
EP
1S
TE
P 2
A,D
,or
NS
Sta
tem
ent
A o
r D
1.A
lgeb
raic
exp
ress
ion
s co
nta
in a
t le
ast
one
vari
able
.A
2.T
he
orde
r of
ope
rati
ons
mu
st b
e fo
llow
ed s
o th
at e
very
ex
pres
sion
wil
l h
ave
only
on
e va
lue.
A
3.A
ll r
eal
nu
mbe
rs a
re i
n t
he
set
of r
atio
nal
nu
mbe
rs.
D4.
Th
e co
mm
uta
tive
pro
pert
y is
tru
e fo
r ad
diti
on a
nd
mu
ltip
lica
tion
on
ly.
A
5.T
he
phra
se t
wic
e th
e su
m o
f a
nu
mbe
r sq
uar
ed a
nd
6 co
uld
be
wri
tten
as
2n2
�6.
D
6.T
he
refl
exiv
e pr
oper
ty o
f eq
ual
ity
stat
es t
hat
if
a�
bth
en
b�
a.D
7.T
he
abso
lute
val
ue
of a
nu
mbe
r is
its
dis
tan
ce f
rom
0 o
n
the
nu
mbe
r li
ne.
A
8.If
th
e ab
solu
te v
alu
e of
an
y ex
pres
sion
is
equ
al t
o a
neg
ativ
e n
um
ber,
then
th
e so
luti
on i
s th
e em
pty
set.
A
9.W
hen
add
ing
or s
ubt
ract
ing
a n
egat
ive
nu
mbe
r to
bot
h s
ides
of a
n i
neq
ual
ity,
the
ineq
ual
ity
sym
bol
mu
st b
e re
vers
ed.
D
10.
Wri
tin
g a
solu
tion
in
th
e fo
rm {
x|x
�5}
is
call
ed s
et b
uil
der
not
atio
n.
A
11.
If a
com
pou
nd
ineq
ual
ity
con
tain
s th
e w
ord
“or”
,th
e so
luti
on
wil
l be
th
e in
ters
ecti
on o
f th
e so
luti
on s
ets
of t
he
two
ineq
ual
itie
s.D
12.
If |
3x�
1|�
10,t
hen
3x
�1
�10
an
d 3a
�1
��
10.
D
STEP
2
Lesson 1-1
Cha
pter
15
Gle
ncoe
Alg
ebra
2
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-1 i
n y
our
text
boo
k.
•N
urs
es u
se t
he
form
ula
F�
to c
ontr
ol t
he
flow
rat
e fo
r IV
s.N
ame
the
quan
tity
th
at e
ach
of
the
vari
able
s in
th
is f
orm
ula
rep
rese
nts
an
d th
e u
nit
s in
wh
ich
each
is
mea
sure
d.
Fre
pres
ents
th
e an
d is
mea
sure
d in
pe
r m
inu
te.
Vre
pres
ents
th
e of
sol
uti
on a
nd
is m
easu
red
in
.
dre
pres
ents
th
e an
d is
mea
sure
d in
pe
r m
illi
lite
r.
tre
pres
ents
an
d is
mea
sure
d in
.
•W
rite
th
e ex
pres
sion
th
at a
nu
rse
wou
ld u
se t
o ca
lcu
late
th
e fl
ow r
ate
of a
n I
V i
f a
doct
oror
ders
135
0 m
illi
lite
rs o
f IV
sal
ine
to b
e gi
ven
ove
r 8
hou
rs,w
ith
a d
rop
fact
or o
f 20
dro
pspe
r m
illi
lite
r.D
o n
ot f
ind
the
valu
e of
th
is e
xpre
ssio
n.
Rea
d t
he
Less
on
1.T
her
e is
a c
ust
omar
y or
der
for
grou
pin
g sy
mbo
ls.B
rack
ets
are
use
d ou
tsid
e of
pare
nth
eses
.Bra
ces
are
use
d ou
tsid
e of
bra
cket
s.Id
enti
fy t
he
inn
erm
ost
expr
essi
on(s
) in
each
of
the
foll
owin
g ex
pres
sion
s.
a.[(
3 �
22)
�8]
�4
(3 �
22)
b.
9 �
[5(8
�6)
�2(
10 �
7)]
(8 �
6) a
nd
(10
�7)
c.{1
4 �
[8 �
(3 �
12)2
]} �
(63
�10
0)(3
�12
)
2.R
ead
the
foll
owin
g in
stru
ctio
ns.
Th
en u
se g
rou
pin
g sy
mbo
ls t
o sh
ow h
ow t
he
inst
ruct
ion
sca
n b
e pu
t in
th
e fo
rm o
f a
mat
hem
atic
al e
xpre
ssio
n.
Mu
ltip
ly t
he
diff
eren
ce o
f 13
an
d 5
by t
he
sum
of
9 an
d 21
.Add
th
e re
sult
to
10.T
hen
divi
de w
hat
you
get
by
2.[(
13 �
5)(9
�21
) �
10]
�2
3.W
hy
is i
t im
port
ant
for
ever
yon
e to
use
th
e sa
me
orde
r of
ope
rati
ons
for
eval
uat
ing
expr
essi
ons?
Sam
ple
an
swer
:If
eve
ryo
ne
did
no
t u
se t
he
sam
e o
rder
of
op
erat
ion
s,d
iffe
ren
t p
eop
le m
igh
t g
et d
iffe
ren
t an
swer
s.
Rem
emb
er W
hat
Yo
u le
arn
ed4.
Th
ink
of a
ph
rase
or
sen
ten
ce t
o h
elp
you
rem
embe
r th
e or
der
of o
pera
tion
s.S
amp
le a
nsw
er:
Ple
ase
excu
se m
y d
ear
Au
nt
Sal
ly.(
par
enth
eses
;ex
po
nen
ts;
mu
ltip
licat
ion
an
d d
ivis
ion
;ad
dit
ion
an
d s
ub
trac
tio
n)
1350
�20
��
8 �
60
min
ute
sti
me
dro
ps
dro
p f
acto
r
mill
ilite
rsvo
lum
e
dro
ps
flo
w r
ateV
�d
t
Less
on R
eadi
ng G
uide
Exp
ress
ion
s an
d F
orm
ula
s
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A1
Chapter 1 A2 Glencoe Algebra 2
Answers (Lesson 1-1)
Cha
pter
16
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
Exp
ress
ion
s an
d F
orm
ula
s
Ord
er o
f O
per
atio
ns
1.S
impl
ify t
he e
xpre
ssio
ns in
side
gro
upin
g sy
mbo
ls.
Ord
er o
f2.
Eva
luat
e al
l pow
ers.
Op
erat
ion
s3.
Do
all m
ultip
licat
ions
and
div
isio
ns f
rom
left
to r
ight
.4.
Do
all a
dditi
ons
and
subt
ract
ions
fro
m le
ft to
rig
ht.
Eva
luat
e [1
8 �
(6 �
4)]
�2.
[18
�(6
�4)
] �
2 �
[18
�10
] �
2�
8 �
2�
4
Eva
luat
e 3x
2�
x(y
�5)
if
x�
3 an
d
y�
0.5.
Rep
lace
eac
h va
riab
le w
ith
the
give
n va
lue.
3x2
�x(
y�
5) �
3
(3)2
�3(
0.5
�5)
�3
(9
) �
3(�
4.5)
�27
�13
.5�
13.5
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.14
�(6
�2)
172.
11 �
(3 �
2)2
�14
3.2
�(4
�2)
3�
64
4.9(
32�
6)13
55.
(5 �
23)2
�52
144
6.52
��
18 �
234
.25
7.�
68.
(7 �
32)2
�62
409.
20 �
22�
611
10.1
2 �
6 �
3 �
2(4)
611
.14
�(8
�20
�2)
�7
12.6
(7)
�4
�4
�5
38
13.8
(42
�8
�32
)�
240
14.
�24
15.
4
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�8.
2,b
��
3,c
�4,
and
d�
�.
16.
49.2
17.5
(6c
�8b
�10
d)
215
18.
�6
19.a
c�
bd31
.320
.(b
�c)
2�
4a81
.821
.�
6b�
5c�
54.4
22.3
���
b�
2123
.cd
�4
24.d
(a�
c)�
6.1
25.a
�b
�c
7.45
26.b
�c
�4
�d
�15
27.
�d
8.7
a b
�c
b dc d
a dc2�
1 b
�d
ab d
1 � 26 �
9 �
3 �
15
8
�2
6 �
4 �
2
4
�6
�1
16 �
23�
4
1
�22
1 4
NA
ME
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____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-1
Exer
cise
s
Exam
ple
1Ex
ampl
e 2
Lesson 1-1
Cha
pter
17
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
Exp
ress
ion
s an
d F
orm
ula
s
Form
ula
sA
for
mu
lais
a m
ath
emat
ical
sen
ten
ce t
hat
use
s va
riab
les
to e
xpre
ss t
he
rela
tion
ship
bet
wee
n c
erta
in q
uan
titi
es.I
f yo
u k
now
th
e va
lue
of e
very
var
iabl
e ex
cept
on
ein
a f
orm
ula
,you
can
use
su
bsti
tuti
on a
nd
the
orde
r of
ope
rati
ons
to f
ind
the
valu
e of
th
eu
nkn
own
var
iabl
e. To
calc
ula
te t
he
nu
mb
er o
f re
ams
of p
aper
nee
ded
to
pri
nt
n
cop
ies
of a
boo
kle
t th
at i
s p
pag
es l
ong,
you
can
use
th
e fo
rmu
la r
�,w
her
e r
is t
he
nu
mb
er o
f re
ams
nee
ded
.How
man
y re
ams
of p
aper
mu
st y
ou b
uy
to p
rin
t 17
2 co
pie
s of
a 2
5-p
age
boo
kle
t?
Su
bsti
tute
n�
172
and
p�
25 i
nto
th
e fo
rmu
la r
�.
r� � �
8.6
You
can
not
bu
y 8.
6 re
ams
of p
aper
.You
wil
l n
eed
to b
uy
9 re
ams
to p
rin
t 17
2 co
pies
.
For
Exe
rcis
es 1
–3,u
se t
he
foll
owin
g in
form
atio
n.
For
a s
cien
ce e
xper
imen
t,S
arah
cou
nts
th
e n
um
ber
of b
reat
hs
nee
ded
for
her
to
blow
up
abe
ach
bal
l.S
he
wil
l th
en f
ind
the
volu
me
of t
he
beac
h b
all
in c
ubi
c ce
nti
met
ers
and
divi
deby
th
e n
um
ber
of b
reat
hs
to f
ind
the
aver
age
volu
me
of a
ir p
er b
reat
h.
1.H
er b
each
bal
l h
as a
rad
ius
of 9
in
ches
.Fir
st s
he
con
vert
s th
e ra
diu
s to
cen
tim
eter
su
sin
g th
e fo
rmu
la C
�2.
54I,
wh
ere
Cis
a l
engt
h i
n c
enti
met
ers
and
Iis
th
e sa
me
len
gth
in i
nch
es.H
ow m
any
cen
tim
eter
s ar
e th
ere
in 9
in
ches
?22
.86
cm
2.T
he
volu
me
of a
sph
ere
is g
iven
by
the
form
ula
V�
�r3
,wh
ere
Vis
th
e vo
lum
e of
th
e
sph
ere
and
ris
its
rad
ius.
Wh
at i
s th
e vo
lum
e of
th
e be
ach
bal
l in
cu
bic
cen
tim
eter
s?(U
se 3
.14
for
�.)
50,0
15 c
m3
3.S
arah
tak
es 4
0 br
eath
s to
blo
w u
p th
e be
ach
bal
l.W
hat
is
the
aver
age
volu
me
of a
ir p
erbr
eath
?ab
ou
t 12
50 c
m3
4.A
per
son
’s b
asal
met
abol
ic r
ate
(or
BM
R)
is t
he
nu
mbe
r of
cal
orie
s n
eede
d to
su
ppor
t h
isor
her
bod
ily
fun
ctio
ns
for
one
day.
Th
e B
MR
of
an 8
0-ye
ar-o
ld m
an i
s gi
ven
by
the
form
ula
BM
R �
12w
�(0
.02)
(6)1
2w,w
her
e w
is t
he
man
’s w
eigh
t in
pou
nds
.Wh
at i
s th
eB
MR
of
an 8
0-ye
ar-o
ld m
an w
ho
wei
ghs
170
pou
nds
?17
95 c
alo
ries
4 3
43,0
00
500
(172
)(25
)
50
0
np
500
np
� 500
NA
ME
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__D
AT
E__
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__P
ER
IOD
____
_
1-1
Exer
cise
s
Exam
ple
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A2
Chapter 1 A3 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-1)
Skill
s Pr
acti
ceE
xpre
ssio
ns
and
For
mu
las
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.18
�2
�3
272.
9 �
6 �
2 �
113
3.(3
�8)
2 (4)
�3
974.
5 �
3(2
�12
�2)
�7
5.�
[�9
�10
(3)]
�7
6.3
7.(1
68 �
7)32
�43
152
8.[3
(5)
�12
8 �
22]5
�85
Eva
luat
e ea
ch e
xpre
ssio
n i
f r
��
1,s
�3,
t�
12,v
�0,
and
w�
�.
9.6r
�2s
010
.2st
�4r
s84
11.w
(s�
r)�
212
.s�
2r�
16v
1
13.(
4s)2
144
14.s
2 r�
wt
�3
15.2
(3r
�w
) �
716
.4
17.�
w[t
�(t
�r)
]18
.0
19.9
r2�
(s2
�1)
t10
520
.7s
�2v
�22
21.T
EMPE
RA
TUR
ET
he
form
ula
K�
C�
273
give
s th
e te
mpe
ratu
re i
n k
elvi
ns
(K)
for
agi
ven
tem
pera
ture
in
deg
rees
Cel
siu
s.W
hat
is
the
tem
pera
ture
in
kel
vin
s w
hen
th
ete
mpe
ratu
re i
s 55
deg
rees
Cel
siu
s?32
8 K
22.T
EMPE
RA
TUR
ET
he
form
ula
C�
(F�
32)
give
s th
e te
mpe
ratu
re i
n d
egre
es C
elsi
us
for
a gi
ven
tem
pera
ture
in
deg
rees
Fah
ren
hei
t.W
hat
is
the
tem
pera
ture
in
deg
rees
Cel
siu
s w
hen
th
e te
mpe
ratu
re i
s 68
deg
rees
Fah
ren
hei
t?20
�C
5 9
2w r
rv3
s225 � 2
3v�
t 5s
�t
1 � 2
6(7
�5)
4
1 3
Cha
pter
18
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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AT
E__
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ER
IOD
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1-1
Lesson 1-1
Cha
pter
19
Gle
ncoe
Alg
ebra
2
Fin
d t
he
valu
e of
eac
h e
xpre
ssio
n.
1.3(
4 �
7) �
11�
202.
4(12
�42
)�
16
3.1
�2
�3(
4) �
2�
34.
12 �
[20
�2(
62�
3 �
22)]
88
5.20
�(5
�3)
�52
(3)
856.
(�2)
3�
(3)(
8) �
(5)(
10)
18
7.18
�{5
�[3
4 �
(17
�11
)]}
418.
[4(5
�3)
�2(
4 �
8)]
�16
1
9.[6
�42
]�
510
.[�
5 �
5(�
3)]
�5
11.
3212
.�
(�1)
2�
4(�
9)�
53
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
�,b
��
8,c
��
2,d
�3,
and
e�
.
13.a
b2�
d45
14.(
c�
d)b
�8
15.
�d
212
16.
12
17.(
b�
de)
e2�
118
.ac3
�b2
de
�70
19.�
b[a
�(c
�d
)2]
206
20.
�22
21.9
bc�
141
22.2
ab2
�(d
3�
c)67
23.T
EMPE
RA
TUR
ET
he
form
ula
F�
C�
32 g
ives
th
e te
mpe
ratu
re i
n d
egre
es
Fah
ren
hei
t fo
r a
give
n t
empe
ratu
re i
n d
egre
es C
elsi
us.
Wh
at i
s th
e te
mpe
ratu
re i
nde
gree
s Fa
hre
nh
eit
wh
en t
he
tem
pera
ture
is
�40
deg
rees
Cel
siu
s?�
40�F
24.P
HY
SIC
ST
he
form
ula
h�
120t
�16
t2gi
ves
the
hei
ght
hin
fee
t of
an
obj
ect
tse
con
dsaf
ter
it i
s sh
ot u
pwar
d fr
om E
arth
’s s
urf
ace
wit
h a
n i
nit
ial
velo
city
of
120
feet
per
seco
nd.
Wh
at w
ill
the
hei
ght
of t
he
obje
ct b
e af
ter
6 se
con
ds?
144
ft
25.A
GR
ICU
LTU
RE
Fait
h o
wn
s an
org
anic
app
le o
rch
ard.
Fro
m h
er e
xper
ien
ce t
he
last
few
seas
ons,
she
has
dev
elop
ed t
he
form
ula
P�
20x
�0.
01x2
�24
0 to
pre
dict
her
pro
fit
Pin
doll
ars
this
sea
son
if
her
tre
es p
rodu
ce x
bush
els
of a
pple
s.W
hat
is
Fait
h’s
pre
dict
edpr
ofit
th
is s
easo
n i
f h
er o
rch
ard
prod
uce
s 30
0 bu
shel
s of
app
les?
$486
0
9 5
1 e
c e2ac
4dd(b
� c
)
acab c
1 � 33 � 4
(�8)
2 5
�9
�8(
13 �
37)
6
1 41 2
Prac
tice
Exp
ress
ion
s an
d F
orm
ula
s
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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AT
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IOD
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1-1
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A3
Chapter 1 A4 Glencoe Algebra 2
Answers (Lesson 1-1)
Wor
d Pr
oble
m P
ract
ice
Exp
ress
ion
s an
d F
orm
ula
s
Cha
pter
110
Gle
ncoe
Alg
ebra
2
1.A
RR
AN
GEM
ENTS
Th
e ch
airs
in
an
audi
tori
um
are
arr
ange
d in
to t
wo
rect
angl
es.B
oth
rec
tan
gles
are
10
row
sde
ep.O
ne
rect
angl
e h
as 6
ch
airs
per
ro
w a
nd
the
oth
er h
as 1
2 ch
airs
per
row
.W
rite
an
exp
ress
ion
for
th
e to
tal
nu
mbe
rof
ch
airs
in
th
e au
dito
riu
m.
10 �
6 �
10 �
12 o
r 10
(6 �
12)
2.G
EOM
ETRY
Th
e fo
rmu
la f
or t
he
area
of
a r
ing-
shap
ed o
bjec
t is
giv
en b
y A
��
(R2
�r2
),w
her
e R
is t
he
radi
us
of t
he
oute
r ci
rcle
an
d r
is t
he
radi
us
of t
he
inn
er c
ircl
e.If
R�
10 i
nch
es a
nd
r�
5in
ches
,wh
at i
s th
e ar
ea r
oun
ded
to t
he
nea
rest
squ
are
inch
?
236
in2
3.G
UES
S A
ND
CH
ECK
Am
anda
re
ceiv
ed a
wor
ksh
eet
from
her
tea
cher
.U
nfo
rtu
nat
ely,
one
of t
he
oper
atio
ns
in a
neq
uat
ion
was
cov
ered
by
a bl
ot.W
hat
oper
atio
n i
s h
idde
n b
y th
e bl
ot?
sub
trac
tio
n
4.G
AS
MIL
EAG
ER
ick
has
ddo
llar
s.T
hefo
rmul
a fo
r th
e nu
mbe
r of
gal
lons
of
gaso
line
tha
t R
ick
can
buy
wit
h d
doll
ars
is g
iven
by
g�
.Th
efo
rmu
la f
or t
he
nu
mbe
r of
mil
es t
hat
Ric
k ca
n d
rive
on
gga
llon
s of
gas
olin
e is
giv
en b
y m
�21
g.H
ow m
any
mil
es c
an R
ick
driv
e on
$8
wor
th o
f ga
soli
ne?
56 m
i
CO
OK
ING
For
Exe
rcis
es 5
an
d 6
,use
the
foll
owin
g in
form
atio
n.
A s
teak
has
th
ickn
ess
win
ches
.Let
Tbe
the
tim
e it
tak
es t
o br
oil
the
stea
k.It
tak
es12
min
ute
s to
bro
il a
on
e in
ch t
hic
k st
eak.
For
eve
ry a
ddit
ion
al i
nch
of
thic
knes
s,th
e st
eak
shou
ld b
e br
oile
d fo
r 5
mor
em
inu
tes.
5.W
rite
a f
orm
ula
for
Tin
ter
ms
of w
.S
amp
le A
nsw
er:
T�
5(w
�1)
�12
or
T�
5w�
7
6.U
se y
our
form
ula
to
com
pute
th
e n
um
ber
of m
inu
tes
it w
ould
tak
e to
bro
il a
2 i
nch
thic
k st
eak.
17 m
in
d 3
10 +
3(4
+ 6
) =
4
rR
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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AT
E__
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ER
IOD
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1-1
Lesson 1-1
Cha
pter
111
Gle
ncoe
Alg
ebra
2
You
are
tra
veli
ng
to y
our
aun
t’s h
ouse
200
mil
es a
way
for
a s
urp
rise
bir
thda
y pa
rty.
Th
e pa
rty
star
ts a
t 3
P.M
.bu
t yo
u c
ann
ot l
eave
fro
m y
our
hou
se b
efor
e 11
A.M
.You
m
ust
fil
l yo
ur
gas
tan
k be
fore
th
e tr
ip.G
asol
ine
is $
3.50
per
gal
lon
an
d yo
u h
ave
$30.
Wil
l yo
u m
ake
it t
o th
e pa
rty
and
mak
e it
bac
k h
ome?
Fir
st d
eter
min
e at
wh
ich
spe
ed y
ou m
ust
tra
vel
to a
rriv
e by
3:0
0.
1.A
sim
ple
form
ula
rel
ates
th
e tr
avel
tim
e,de
pen
din
g on
you
r av
erag
e sp
eed
in
mil
es p
er h
our
(mph
),T
�,w
her
e T
is t
ime
in h
ours
,Dis
th
e di
stan
ce (
200
mil
es),
and
Sis
th
e sp
eed.
Det
erm
ine
trav
el t
ime
to y
our
aun
t’s h
ouse
at
vari
ous
spee
ds.
2.F
or w
hic
h s
peed
(s),
wil
l yo
u m
iss
the
surp
rise
bir
thda
y pa
rty?
You
will
mis
s th
e p
arty
fo
r al
l sp
eed
s 50
mp
h a
nd
less
,ass
um
ing
an
11
A.M
.dep
artu
re.
Now
det
erm
ine
if y
ou c
an a
ffor
d en
ough
gas
olin
e to
mak
e th
e tr
ip a
nd
retu
rn.
3.H
ow m
any
gall
ons
of g
as c
an y
ou b
uy?
Ab
ou
t 8.
5 g
allo
ns
4.C
ost
depe
nds
on
th
e co
st o
f ga
soli
ne,
the
nu
mbe
r of
tot
al m
iles
of
the
trip
,an
d yo
ur
car’
s fu
el e
ffic
ien
cy (
mi/g
al).
Th
e m
iles
per
gal
lon
can
be
fou
nd
usi
ng
the
form
ula
M�
�S
2�
S,w
her
e S
is y
our
spee
d.D
eter
min
e yo
ur
fuel
rat
e fo
r
the
spee
ds n
eede
d to
get
to
you
r au
nt’s
.Wil
l yo
u m
ake
it?
You
can
mak
e it
to
yo
ur
aun
t’s h
ou
se o
n t
ime,
but
wo
n’t
hav
e en
ou
gh
gas
to
get
ho
me.
5 21 30
D S
Sp
eed
(m
ph
)T
ime
(ho
urs
)
355.
740
5.0
454.
450
4.0
553.
660
3.3
653.
070
2.8
752.
6
Enri
chm
ent
Trav
elin
g o
n a
Bu
dg
et
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
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____
____
____
____
____
____
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AT
E__
____
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ER
IOD
____
_
1-1
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A4
Chapter 1 A5 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-2)
Cha
pter
112
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Pro
per
ties
of
Rea
l Nu
mb
ers
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-2 i
n y
our
text
boo
k.
•W
hy
are
all
of t
he
amou
nts
lis
ted
on t
he
regi
ster
sli
p at
th
e to
p of
th
e pa
ge f
ollo
wed
by
neg
ativ
e si
gns?
Sam
ple
an
swer
:Th
e am
ou
nt
of
each
co
up
on
is s
ub
trac
ted
fro
m t
he
tota
l am
ou
nt
of
pu
rch
ases
so
th
at y
ou
sav
e m
on
ey b
y u
sin
gco
up
on
s.•
Des
crib
e tw
o w
ays
of c
alcu
lati
ng
the
amou
nt
of m
oney
you
sav
ed b
y u
sin
g co
upo
ns
if y
our
regi
ster
sli
p is
th
e on
e sh
own
on
pag
e 11
.S
amp
le a
nsw
er:
Ad
d a
ll th
e in
div
idu
alco
up
on
am
ou
nts
or
add
th
e am
ou
nts
fo
r th
e sc
ann
ed c
ou
po
ns
and
mu
ltip
ly t
he
sum
by
2.
Rea
d t
he
Less
on
1.R
efer
to
the
Key
Con
cept
s bo
x on
pag
e 11
.Th
e n
um
bers
2.5�
7�an
d 0.
0100
1000
1… b
oth
invo
lve
deci
mal
s th
at “
go o
n f
orev
er.”
Exp
lain
wh
y on
e of
th
ese
nu
mbe
rs i
s ra
tion
al a
nd
the
oth
er i
s ir
rati
onal
.S
amp
le a
nsw
er:
2.5�7�
�2.
5757
… is
a r
epea
tin
gd
ecim
al b
ecau
se t
her
e is
a b
lock
of
dig
its,
57,t
hat
rep
eats
fo
reve
r,so
this
nu
mb
er is
rat
ion
al.T
he
nu
mb
er 0
.010
0100
01…
is a
no
n-r
epea
tin
gd
ecim
al b
ecau
se,a
lth
ou
gh
th
e d
igit
s fo
llow
a p
atte
rn,t
her
e is
no
blo
cko
f d
igit
s th
at r
epea
ts.S
o t
his
nu
mb
er is
an
irra
tio
nal
nu
mb
er.
2.W
rite
th
e A
ssoc
iati
ve P
rope
rty
of A
ddit
ion
in
sym
bols
.Th
en i
llu
stra
te t
his
pro
pert
y by
fin
din
g th
e su
m 1
2 �
18 �
45 i
n t
wo
diff
eren
t w
ays.
(a�
b)
�c
�a
�(b
�c)
;S
amp
le a
nsw
er:
(12
�18
) �
45 �
30 �
45 �
75;
12 �
(18
�45
) �
12 �
63 �
75
3.C
onsi
der
the
equ
atio
ns
(a
b)
c�
a
(b
c) a
nd
(a
b)
c�
c
(a
b).O
ne
of t
he
equ
atio
ns
use
s th
e A
ssoc
iati
ve P
rope
rty
of M
ult
ipli
cati
on a
nd
one
use
s th
e C
omm
uta
tive
Pro
pert
y of
Mu
ltip
lica
tion
.How
can
you
tel
l w
hic
h p
rope
rty
is b
ein
g u
sed
in e
ach
equ
atio
n?
Th
e fir
st e
qu
atio
n u
ses
the
Ass
oci
ativ
e P
rop
erty
of
Mu
ltip
licat
ion
.T
he
qu
antit
ies
a,b
,an
d c
are
use
d in
th
e sa
me
ord
er,b
ut
they
are
gro
up
edd
iffer
ently
on
th
e tw
o s
ides
of
the
equ
atio
n.T
he
seco
nd
eq
uat
ion
use
s th
eq
uan
titie
s in
diff
eren
t o
rder
s o
n t
he
two
sid
es o
f th
e eq
uat
ion
.So
th
ese
con
d e
qu
atio
n u
ses
the
Co
mm
uta
tive
Pro
per
ty o
f M
ulti
plic
atio
n.
Rem
emb
er W
hat
Yo
u L
earn
ed4.
How
can
th
e m
ean
ings
of
the
wor
ds c
omm
ute
ran
d as
soci
atio
nh
elp
you
to
rem
embe
r th
edi
ffer
ence
bet
wee
n t
he
com
mu
tati
ve a
nd
asso
ciat
ive
prop
erti
es?
Sam
ple
an
swer
:A
co
mm
ute
r is
so
meo
ne
wh
o t
rave
ls b
ack
and
fo
rth
to
wo
rk o
r an
oth
erp
lace
,an
d t
he
com
mu
tati
ve p
rop
erty
say
s yo
u c
an s
wit
ch t
he
ord
erw
hen
two
nu
mb
ers
that
are
bei
ng
ad
ded
or
mu
ltip
lied
.An
ass
oci
atio
n is
ag
rou
p o
f p
eop
le w
ho
are
co
nn
ecte
d o
r u
nit
ed,a
nd
th
e as
soci
ativ
ep
rop
erty
say
s th
at y
ou
can
sw
itch
th
e g
rou
pin
gw
hen
th
ree
nu
mb
ers
are
add
ed o
r m
ult
iplie
d.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-2
Cha
pter
113
Gle
ncoe
Alg
ebra
2
Stud
y G
uide
and
Inte
rven
tion
Pro
per
ties
of
Rea
l Nu
mb
ers
Rea
l Nu
mb
ers
All
rea
l n
um
bers
can
be
clas
sifi
ed a
s ei
ther
rat
ion
al o
r ir
rati
onal
.Th
e se
t of
rat
ion
al n
um
bers
in
clu
des
seve
ral
subs
ets:
nat
ura
l n
um
bers
,wh
ole
nu
mbe
rs,
and
inte
gers
.
Rre
al n
umbe
rs{a
ll ra
tiona
ls a
nd ir
ratio
nals
}
Qra
tiona
l num
bers
{all
num
bers
tha
t ca
n be
rep
rese
nted
in t
he f
orm
,
whe
re m
and
nar
e in
tege
rs a
nd
nis
not
equ
al t
o 0}
Iirr
atio
nal n
umbe
rs{a
ll no
nter
min
atin
g, n
onre
peat
ing
deci
mal
s}
Nna
tura
l num
bers
{1,
2, 3
, 4,
5,
6, 7
, 8,
9,
…}
Ww
hole
num
bers
{0,
1, 2
, 3,
4,
5, 6
, 7,
8,
…}
Zin
tege
rs{…
, �
3, �
2, �
1, 0
, 1,
2,
3, …
}
Nam
e th
e se
ts o
f n
um
ber
s to
wh
ich
eac
h n
um
ber
bel
ongs
.
a.�
rati
onal
s (Q
),re
als
(R)
b.
�25�
�25�
�5
nat
ura
ls (
N),
wh
oles
(W
),in
tege
rs (
Z),
rati
onal
s (Q
),re
als
(R)
Nam
e th
e se
ts o
f n
um
ber
s to
wh
ich
eac
h n
um
ber
bel
ongs
.
1.Q
,R2.
��
81�Z
,Q,R
3.0
W,Z
,Q,R
4.19
2.00
05Q
,R
5.73
N,W
,Z,Q
,R
6.34
Q,R
7.Q
,R8.
26.1
Q,R
9.�
I,R
10.
N,W
,Z,Q
,R11
.�4.
1�7�Q
,R
12.
N,W
,Z,Q
,R13
.�1
Z,Q
,R14
.�42�
I,R
15.�
11.2
Q,R
16.�
Q,R
17.
I,R
18.3
3.3�
Q,R
19.8
94,0
00N
,W,Z
,Q,R
20.�
0.02
Q,R
�5�
2
8 13
�25�
5
15 3
�36�
9
1 2
6 7
11 � 3
m n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
Exam
ple
Exer
cise
s
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A5
Chapter 1 A6 Glencoe Algebra 2
Answers (Lesson 1-2)
Cha
pter
114
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Pro
per
ties
of
Rea
l Nu
mb
ers
Rea
l Nu
mb
er P
rop
erti
es
For
any
rea
l num
bers
a,
b, a
nd c
Pro
per
tyA
dd
itio
nM
ult
iplic
atio
n
Com
mut
ativ
ea
�b
�b
�a
a
b�
b
a
Ass
ocia
tive
(a�
b) �
c�
a�
(b�
c)(a
b)
c
�a
(b
c)
Iden
tity
a�
0 �
a�
0 �
aa
1
�a
�1
a
Inve
rse
a�
(�a)
�0
�(�
a) �
aIf
ais
not
zer
o, t
hen
a
�1
�
a.
Dis
trib
utiv
ea(
b�
c) �
ab�
acan
d (b
�c)
a�
ba�
ca
Sim
pli
fy 9
x�
3y�
12y
�0.
9x.
9x�
3y�
12y
�0.
9x�
9x�
(�0.
9x)
�3y
�12
yC
omm
utat
ive
Pro
pert
y (�
)
�(9
�(�
0.9)
)x�
(3 �
12)y
Dis
trib
utiv
e P
rope
rty
�8.
1x�
15y
Sim
plify
.
Sim
pli
fy e
ach
exp
ress
ion
.
1.8(
3a�
b) �
4(2b
�a)
2.40
s�
18t
�5t
�11
s3.
(4j
�2k
�6j
�3k
)
20a
51s
�13
tk
�j
4.10
(6g
�3h
) �
4(5g
�h
)5.
12�
��
6.8(
2.4r
�3.
1s)
�6(
1.5r
�2.
4s)
80g
�26
h4a
� 3
b10
.2r
�39
.2s
7.4(
20 �
4p)
�(4
�16
p)8.
5.5j
�8.
9k�
4.7k
�10
.9j
9.1.
2(7x
�5)
�(1
0 �
4.3x
)
77 �
4p4.
2k�
5.4j
12.7
x�
16
10.9
(7e
�4f
) �
0.6(
e�
5f)
11.2
.5m
(12
�8.
5)12
.p
�r
�r
�p
62.4
e�
39f
8.75
mp
�r
13.4
(10g
�80
h)
�20
(10h
�5g
)14
.2(1
5 �
45c)
�(1
2 �
18c)
140g
�12
0h40
�10
5c
15.(
7 �
2.1x
)3 �
2(3.
5x�
6)16
.(1
8 �
6n�
12 �
3n)
0.7x
�9
20 �
2n
17.1
4(j
�2)
�3j
(4 �
7)18
.50(
3a�
b) �
20(b
�2a
)2j
�7
190a
�70
b
2 3
5 6
4 � 51 � 4
1 23 5
1 53 4
3 4
b 4a 3
2 � 5
1 51 a1 a
Stud
y G
uide
and
Inte
rven
tion
(con
tinue
d)
Pro
per
ties
of
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
Exer
cise
s
Exam
ple
Skill
s Pr
acti
ceP
rop
erti
es o
f R
eal N
um
ber
s
Lesson 1-2
Cha
pter
115
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Nam
e th
e se
ts o
f n
um
ber
s to
wh
ich
eac
h n
um
ber
bel
ongs
.
1.34
N,W
,Z,Q
,R2.
�52
5Z
,Q,R
3.0.
875
Q,R
4.N
,W,Z
,Q,R
5.�
�9�
Z,Q
,R6.
�30�
I,R
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch e
qu
atio
n.
7.3
x
�x
3
8.3a
�0
�3a
Co
mm
.(�
)A
dd
.Id
en.
9.2(
r�
w)
�2r
�2w
10.2
r�
(3r
�4r
) �
(2r
�3r
) �
4rD
istr
ibu
tive
Ass
oc.
(�)
11.5
y ���
112
.15x
(1)
�15
x
Mu
lt.I
nv.
Mu
lt.I
den
.
13.0
.6[2
5(0.
5)]
�[0
.6(2
5)]0
.514
.(10
b�
12b)
�7b
�(1
2b�
10b)
�7b
Ass
oc.
(�)
Co
mm
.(�
)
Nam
e th
e ad
dit
ive
inve
rse
and
mu
ltip
lica
tive
in
vers
e fo
r ea
ch n
um
ber
.
15.1
5 �
15,
16.1
.25
�1.
25,0
.8
17.�
,�18
.3�
3,
Sim
pli
fy e
ach
exp
ress
ion
.
19.3
x�
5 �
2x�
35x
�2
20.x
�y
�z
�y
�x
�z
0
21.�
(3g
�3h
) �
5g�
10h
2g�
13h
22.a
2�
a�
4a�
3a2
�1
�2a
2�
3a�
1
23.3
(m�
z) �
5(2m
�z)
13m
�8z
24.2
x�
3y�
(5x
�3y
�2z
)�
3x�
2z
25.6
(2 �
v) �
4(2v
�1)
8 �
2v26
.(1
5d�
3) �
(8 �
10d
)10
d�
31 2
1 3
4 � 153 � 4
3 45 � 4
4 � 54 5
1 � 15
1 5y
12 3
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A6
Chapter 1 A7 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-2)
Cha
pter
116
Gle
ncoe
Alg
ebra
2
Nam
e th
e se
ts o
f n
um
ber
s to
wh
ich
eac
h n
um
ber
bel
ongs
.
1.64
252.
�7�
3.2�
4.0
N,W
,Z,Q
,RI,
RI,
RW
,Z,Q
,R
5.��
Q,R
6.�
�16�
Z,Q
,R7.
�35
Z,Q
,R8.
�31
.8Q
,R
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch e
qu
atio
n.
9.5x
(4
y�
3x)
�5x
(3
x�
4y)
10.7
x�
(9x
�8)
�(7
x�
9x)
�8
Co
mm
.(�
)A
sso
c.(�
)
11.5
(3x
�y)
�5(
3x�
1y)
12.7
n�
2n�
(7 �
2)n
Mu
lt.I
den
.D
istr
ibu
tive
13.3
(2x)
y�
(3
2)(x
y)14
.3x
2y
�3
2
x
y
15.(
6 �
�6)
y�
0y
Ass
oc.
(�)
Co
mm
.(�
)A
dd
.Inv
.
16.
4y
�1y
17.5
(x�
y) �
5x�
5y18
.4n
�0
�4n
Mu
lt.I
nv.
Dis
trib
uti
veA
dd
.Id
en.
Nam
e th
e ad
dit
ive
inve
rse
and
mu
ltip
lica
tive
in
vers
e fo
r ea
ch n
um
ber
.
19.0
.4�
0.4,
2.5
20.�
1.6
1.6,
�0.
625
21.�
,�22
.5�
5,
Sim
pli
fy e
ach
exp
ress
ion
.
23.5
x�
3y�
2x�
3y3x
24.�
11a
�13
b�
7a�
3b�
4a�
16b
25.8
x�
7y�
(3 �
6y)
8x�
y�
326
.4c
�2c
�(4
c�
2c)
�4c
27.3
(r�
10s)
�4(
7s�
2r)
�5r
�58
s28
.(1
0a�
15)
�(8
�4a
)4a
�1
29.2
(4 �
2x�
y) �
4(5
�x
�y)
30.
�x
�12
y ��
(2x
�12
y)
�12
�8x
�6y
13y
31.T
RA
VEL
Oli
via
driv
es h
er c
ar a
t 60
mil
es p
er h
our
for
th
ours
.Ian
dri
ves
his
car
at
50 m
iles
per
hou
r fo
r (t
�2)
hou
rs.W
rite
a s
impl
ifie
d ex
pres
sion
for
th
e su
m o
f th
edi
stan
ces
trav
eled
by
the
two
cars
.(1
10t
�10
0) m
i
32.N
UM
BER
TH
EORY
Use
th
e pr
oper
ties
of
real
nu
mbe
rs t
o te
ll w
het
her
th
e fo
llow
ing
stat
emen
t is
tru
e or
fal
se:I
f a
�b,
it f
ollo
ws
that
a�
��b �
�.Exp
lain
you
r re
ason
ing.
fals
e;co
un
tere
xam
ple
:5�
��4�
�1 � 4
1 � 5
1 b1 a
1 43 5
5 6
1 21 5
6 � 355 � 6
5 616 � 11
11 � 1611 16
1 4
25 36
Prac
tice
P
rop
erti
es o
f R
eal N
um
ber
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-2
Cha
pter
117
Gle
ncoe
Alg
ebra
2
1.M
ENTA
L M
ATH
Wh
en t
each
ing
elem
enta
ry s
tude
nts
to
mu
ltip
ly a
nd
lear
n p
lace
val
ue,
book
s of
ten
sh
ow
that
54
�8
�(5
0 �
4) �
8 �
(50
�8)
�(4
�8)
.Wh
at p
rope
rty
is u
sed?
Dis
trib
uti
ve P
rop
erty
2.M
OD
ELS
Wh
at p
rope
rty
of r
eal
nu
mbe
rs i
s il
lust
rate
d by
th
e fi
gure
belo
w?
Co
mm
uta
tive
Pro
per
ty o
fM
ult
iplic
atio
n
3.V
ENN
DIA
GR
AM
SM
ake
a V
enn
diag
ram
th
at s
how
s th
e re
lati
onsh
ipbe
twee
n n
atu
ral
nu
mbe
rs,i
nte
gers
,ra
tion
al n
um
bers
,irr
atio
nal
nu
mbe
rs,
and
real
nu
mbe
rs.
4.N
UM
BER
TH
EORY
Con
side
r th
efo
llow
ing
two
stat
emen
ts.
I.T
he
prod
uct
of
any
two
rati
onal
nu
mbe
rs i
s al
way
s an
oth
er r
atio
nal
nu
mbe
r.II
.Th
e pr
odu
ct o
f tw
o ir
rati
onal
nu
mbe
rsis
alw
ays
irra
tion
al.
Det
erm
ine
if t
hes
e st
atem
ents
are
alw
ays,
som
etim
es,o
r n
ever
tru
e.E
xpla
in.
I.al
way
s
II.s
om
etim
es,
�2�
· �2 �
�2
RIG
HT
TRIA
NG
LES
For
Exe
rcis
es 5
–7,
use
th
e fo
llow
ing
info
rmat
ion
.
Th
e le
ngt
hs
of t
he
side
s of
th
e ri
ght
tria
ngl
esh
own
are
rel
ated
by
the
form
ula
c2
= a2
�b2
.
For
eac
h s
et o
f va
lues
for
aan
d b,
dete
rmin
e th
e va
lue
of c
.Sta
te w
het
her
c
is a
nat
ura
l n
um
ber.
5.a
�5,
b�
12c
�13
;it
is a
nat
ura
l nu
mb
er.
6.a
�7,
b�
14c
��
245
�o
r 7�
5�;it
is n
ot
a n
atu
ral n
um
ber
.
7.a
�7,
b�
24c
�25
;it
is a
nat
ura
l nu
mb
er.
ac
b
Rea
l Nu
mb
ers
Irra
tio
nal
s
Rat
ion
als
Inte
ger
s
Nat
ura
lN
um
ber
s
10
7
7
10
=
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wor
d Pr
oble
m P
ract
ice
Pro
per
ties
of
Rea
l Nu
mb
ers
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A7
Chapter 1 A8 Glencoe Algebra 2
Answers (Lessons 1-2 and 1-3)
Cha
pter
118
Gle
ncoe
Alg
ebra
2
Pro
per
ties
of
a G
rou
pA
set
of
nu
mbe
rs f
orm
s a
grou
p w
ith
res
pect
to
an o
pera
tion
if
for
that
ope
rati
onth
e se
t h
as (
1) t
he
Clo
sure
Pro
pert
y,(2
) th
e A
ssoc
iati
ve P
rope
rty,
(3)
a m
embe
rw
hich
is a
n id
enti
ty,a
nd (
4) a
n in
vers
e fo
r ea
ch m
embe
r of
the
set
.
Doe
s th
e se
t {0
,1,2
,3,…
} fo
rm a
gro
up
wit
h r
esp
ect
to a
dd
itio
n?
Clo
sure
Pro
per
ty:
For
all
nu
mbe
rs i
n t
he
set,
is a
�b
in t
he
set?
0 �
1 �
1,an
d 1
isin
th
e se
t;0
�2
�2,
and
2 is
in
th
e se
t;an
d so
on
.Th
e se
t h
ascl
osu
re f
or a
ddit
ion
.
Ass
ocia
tive
Pro
per
ty:
For
all
nu
mbe
rs i
n t
he
set,
does
a�
(b�
c) �
(a�
b) �
c?
0 �
(1 �
2) �
(0 �
1) �
2;1
�(2
�3)
�(1
�2)
�3;
and
so o
n.
Th
e se
t is
ass
ocia
tive
for
add
itio
n.
Iden
tity
:Is
th
ere
som
e n
um
ber,
i,in
th
e se
t su
ch t
hat
i�
a�
a�
a�
ifo
r al
la?
0 �
1 �
1 �
1 �
0;0
�2
�2
�2
�0;
and
so o
n.
Th
e id
enti
ty f
or a
ddit
ion
is
0.
Inve
rse:
Doe
s ea
ch n
um
ber,
a,h
ave
an i
nve
rse,
a�, s
uch
th
at
a��
a�
a�
a��
i? T
he
inte
ger
inve
rse
of 3
is
�3
sin
ce
�3
�3
�0,
and
0 is
th
e id
enti
ty f
or a
ddit
ion
.Bu
t th
e se
t do
es n
otco
nta
in �
3.T
her
efor
e,th
ere
is n
o in
vers
e fo
r 3.
The
set
is
not
a gr
oup
wit
h re
spec
t to
add
itio
n be
caus
e on
ly t
hree
of
the
four
pro
pert
ies
hold
.
Is t
he
set
{�1,
1} a
gro
up
wit
h r
esp
ect
to m
ult
ipli
cati
on?
Clo
sure
Pro
per
ty:
(�1)
(�1)
�1;
(�1)
(1)
��
1;(1
)(�
1) �
�1;
(1)(
1) �
1T
he
set
has
clo
sure
for
mu
ltip
lica
tion
.
Ass
ocia
tive
Pro
per
ty:
(�1)
[(�
1)(�
1)]
�(�
1)(1
) �
�1;
and
so o
nT
he
set
is a
ssoc
iati
ve f
or m
ult
ipli
cati
on.
Iden
tity
:1(
�1)
��
1;1(
1) �
1T
he
iden
tity
for
mu
ltip
lica
tion
is
1.
Inve
rse:
�1
is t
he
inve
rse
of �
1 si
nce
(�
1)(�
1) �
1,an
d 1
is t
he
iden
tity
.1
is t
he
inve
rse
of 1
sin
ce (
1)(1
) �
1,an
d 1
is t
he
iden
tity
.E
ach
mem
ber
has
an
in
vers
e.
Th
e se
t {�
1,1}
is
a gr
oup
wit
h r
espe
ct t
o m
ult
ipli
cati
on b
ecau
se a
ll f
our
prop
erti
es h
old.
Tel
l w
het
her
th
e se
t fo
rms
a gr
oup
wit
h r
esp
ect
to t
he
give
n o
per
atio
n.
1.{i
nte
gers
},ad
diti
onye
s2.
{in
tege
rs},
mu
ltip
lica
tion
no
3.�1 2 ,
2 2 ,3 2 ,
…�,a
ddit
ion
no
4.{m
ult
iple
s of
5},
mu
ltip
lica
tion
no
5.{x
,x2 ,
x3,x
4 ,…
} ad
diti
onn
o6.
{�1�,
�2�,
�3�,
…},
mu
ltip
lica
tion
no
7.{i
rrat
ion
al n
um
bers
},ad
diti
onn
o8.
{rat
ion
al n
um
bers
},ad
diti
onye
s
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1
Exam
ple
2
Lesson 1-3
Cha
pter
119
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Less
on R
eadi
ng G
uide
Sol
vin
g E
qu
atio
ns
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-3 i
n y
our
text
boo
k.
•T
o fi
nd
you
r ta
rget
hea
rt r
ate,
wh
at t
wo
piec
es o
f in
form
atio
n m
ust
you
su
pply
?ag
e (A
)an
d d
esir
ed in
ten
sity
leve
l (I)
•W
rite
an
equ
atio
n t
hat
sh
ows
how
to
calc
ula
te y
our
targ
et h
eart
rat
e.
P�
or
P�
(220
�A
)
I�
6
Rea
d t
he
Less
on
1.a.
How
are
alg
ebra
ic e
xpre
ssio
ns
and
equ
atio
ns
alik
e?S
amp
le a
nsw
er:
Bo
th c
on
tain
var
iab
les,
con
stan
ts,a
nd
op
erat
ion
sig
ns.
b.
How
are
alg
ebra
ic e
xpre
ssio
ns
and
equ
atio
ns
diff
eren
t?S
amp
le a
nsw
er:
Eq
uat
ion
s co
nta
in e
qu
al s
ign
s;ex
pre
ssio
ns
do
no
t.
c.H
ow a
re a
lgeb
raic
exp
ress
ion
s an
d eq
uat
ion
s re
late
d?S
amp
le a
nsw
er:
An
eq
uat
ion
is a
sta
tem
ent
that
say
s th
at t
wo
alg
ebra
ic e
xpre
ssio
ns
are
equ
al.
Rea
d t
he
foll
owin
g p
rob
lem
an
d t
hen
wri
te a
n e
qu
atio
n t
hat
you
cou
ld u
se t
oso
lve
it.D
o n
ot a
ctu
ally
sol
ve t
he
equ
atio
n.I
n y
our
equ
atio
n,l
et m
be
the
nu
mb
erof
mil
es d
rive
n.
2.W
hen
Lou
isa
ren
ted
a m
ovin
g tr
uck
,sh
e ag
reed
to
pay
$28
per
day
plu
s $0
.42
per
mil
e.If
sh
e ke
pt t
he
tru
ck f
or 3
day
s an
d th
e re
nta
l ch
arge
s (w
ith
out
tax)
wer
e $1
53.7
2,h
owm
any
mil
es d
id L
ouis
a dr
ive
the
tru
ck?
3(28
) �
0.42
m�
153.
72
Rem
emb
er W
hat
Yo
u L
earn
ed
3.H
ow c
an t
he
wor
ds r
efle
ctio
nan
d sy
mm
etry
hel
p yo
u r
emem
ber
and
dist
ingu
ish
bet
wee
nth
e re
flex
ive
and
sym
met
ric
prop
erti
es o
f eq
ual
ity?
Th
ink
abou
t h
ow t
hes
e w
ords
are
use
d in
eve
ryda
y li
fe o
r in
geo
met
ry.
Sam
ple
an
swer
:Wh
en y
ou
loo
k at
yo
ur
refl
ecti
on
,yo
u a
re lo
oki
ng
at
you
rsel
f.T
he
refl
exiv
e p
rop
erty
say
s th
at e
very
nu
mb
er is
eq
ual
to
itse
lf.
In g
eom
etry
,sym
met
ry w
ith
res
pec
t to
a li
ne
mea
ns
that
th
e p
arts
of
afi
gu
re o
n t
he
two
sid
es o
f a
line
are
iden
tica
l.T
he
sym
met
ric
pro
per
ty o
feq
ual
ity
allo
ws
you
to
inte
rch
ang
e th
e tw
o s
ides
of
an e
qu
atio
n.T
he
equ
al s
ign
is li
ke t
he
line
of
sym
met
ry.
(220
�A
)
I�
� 6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A8
Chapter 1 A9 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-3)
Cha
pter
120
Gle
ncoe
Alg
ebra
2
Stud
y G
uide
and
Inte
rven
tion
Sol
vin
g E
qu
atio
ns
Ver
bal
Exp
ress
ion
s to
Alg
ebra
ic E
xpre
ssio
ns
Th
e ch
art
sugg
ests
som
e w
ays
toh
elp
you
tra
nsl
ate
wor
d ex
pres
sion
s in
to a
lgeb
raic
exp
ress
ion
s.A
ny
lett
er c
an b
e u
sed
tore
pres
ent
a n
um
ber
that
is
not
kn
own
.
Wo
rd E
xpre
ssio
nO
per
atio
n
and,
plu
s, s
um,
incr
ease
d by
, m
ore
than
addi
tion
min
us,
diffe
renc
e, d
ecre
ased
by,
less
tha
nsu
btra
ctio
n
times
, pr
oduc
t, of
(as
in
of a
num
ber)
mul
tiplic
atio
n
divi
ded
by,
quot
ient
divi
sion
1 2
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.th
e su
m o
f si
x ti
mes
a n
um
ber
and
256n
25
2.fo
ur
tim
es t
he
sum
of
a n
um
ber
and
34(
n�
3)
3.7
less
th
an f
ifte
en t
imes
a n
um
ber
15n
� 7
4.th
e di
ffer
ence
of
nin
e ti
mes
a n
um
ber
and
the
quot
ien
t of
6 a
nd
the
sam
e n
um
ber9n
�
5.th
e su
m o
f 10
0 an
d fo
ur
tim
es a
nu
mbe
r10
0 �
4n
6.th
e pr
odu
ct o
f 3
and
the
sum
of
11 a
nd
a n
um
ber
3(11
�n
)
7.fo
ur
tim
es t
he
squ
are
of a
nu
mbe
r in
crea
sed
by f
ive
tim
es t
he
sam
e n
um
ber
4n2
�5n
8.23
mor
e th
an t
he
prod
uct
of
7 an
d a
nu
mbe
r7n
�23
Wri
te a
ver
bal
sen
ten
ce t
o re
pre
sen
t ea
ch e
qu
atio
n.
Sam
ple
an
swer
s ar
e g
iven
.
9.3n
�35
�79
Th
e d
iffe
ren
ce o
f th
ree
tim
es a
nu
mb
er a
nd
35
is e
qu
al t
o 7
9.
10.2
(n3
�3n
2 ) �
4nTw
ice
the
sum
of
the
cub
e o
f a
nu
mb
er a
nd
th
ree
tim
es t
he
squ
are
of
the
nu
mb
er is
eq
ual
to
fo
ur
tim
es t
he
nu
mb
er.
11.
n5 �n
3
�n
�8
Th
e q
uo
tien
t o
f fi
ve t
imes
a n
um
ber
an
d t
he
sum
of
the
nu
mb
eran
d 3
is e
qu
al t
o t
he
dif
fere
nce
of
the
nu
mb
er a
nd
8.6 � n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
18 l
ess
than
the
qu
otie
nt
of a
nu
mb
er a
nd
3.
�18
n 3
Wri
te a
ver
bal
sen
ten
ce t
ore
pre
sen
t 6(
n�
2) �
14.
Six
tim
es t
he
diff
eren
ce o
f a
nu
mbe
r an
d tw
ois
equ
al t
o 14
.
Exam
ple
2Ex
ampl
e 1
Exer
cise
s
Lesson 1-3
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Pro
per
ties
of
Equ
alit
yYo
u c
an s
olve
equ
atio
ns
by u
sin
g ad
diti
on,s
ubt
ract
ion
,m
ult
ipli
cati
on,o
r di
visi
on.
Ad
dit
ion
an
d S
ub
trac
tio
nF
or a
ny r
eal n
umbe
rs a
, b,
and
c,
if a
�b,
Pro
per
ties
of
Eq
ual
ity
then
a�
c�
b�
can
d a
�c
�b
�c.
Mu
ltip
licat
ion
an
d D
ivis
ion
For
any
rea
l num
bers
a,
b, a
nd c
,if
a�
b,
Pro
per
ties
of
Eq
ual
ity
then
a
c�
b
can
d, if
cis
not
zer
o,
�.
b ca c
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Sol
vin
g E
qu
atio
ns
Sol
ve 1
00 �
8x�
140.
100
�8x
�14
010
0 �
8x�
100
�14
0 �
100
�8x
�40
x�
�5
Sol
ve 4
x�
5y�
100
for
y.
4x�
5y�
100
4x�
5y�
4x�
100
�4x
5y�
100
�4x
y�
(100
�4x
)
y�
20 �
x4 5
1 5
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
1.3s
�45
152.
17 �
9 �
a�
83.
5t�
1 �
6t�
54
4.m
�5.
7 �
x�
38
6.�
8 �
�2(
z�
7)�
3
7.0.
2b�
1050
8.3x
�17
�5x
�13
159.
5(4
�k)
��
10k
�4
10.1
20 �
y�
6080
11.
n�
98 �
n28
12.4
.5 �
2p�
8.7
2.1
13.4
n�
20 �
53 �
2n5
14.1
00 �
20 �
5r�
1615
.2x
�75
�10
2 �
x9
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
16.a
�3b
�c,
for
bb
�17
.�
10,f
or t
t�
18.h
�12
g�
1,fo
r g
g�
19.
�12
,for
pp
�
20.2
xy�
x�
7,fo
r x
x�
21.
��
6,fo
r f
f�
24 �
2d
22.3
(2j
�k)
�10
8,fo
r j
j�18
�23
.3.5
s�
42 �
14t,
for
ss
�4t
�12
24.
�5m
�20
,for
mm
�25
.4x
�3y
�10
,for
yy
�x
�10 � 3
4 � 320
n� 5n
�1
m n
k � 2
f 4d 2
7� 2y
�1
4r � q3p
q
rh
�1
�12
s � 20s 2t
a�
c�
3
1 � 2
5 23 4
1 23 � 4
1 22 3
Cha
pter
121
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Exam
ple
2Ex
ampl
e 1
Exer
cise
s
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A9
Chapter 1 A10 Glencoe Algebra 2
Answers (Lesson 1-3)
Cha
pter
122
Gle
ncoe
Alg
ebra
2
Skill
s Pr
acti
ceS
olvi
ng
Eq
uat
ion
s
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.4
tim
es a
nu
mbe
r,in
crea
sed
by 7
2.8
less
th
an 5
tim
es a
nu
mbe
r
4n�
75n
�8
3.6
tim
es t
he
sum
of
a n
um
ber
and
54.
the
prod
uct
of 3
and
a n
umbe
r,di
vide
d by
9
6(n
�5)
5.3
tim
es t
he
diff
eren
ce o
f 4
and
a n
um
ber
3(4
�n
)
6.th
e pr
odu
ct o
f �
11 a
nd
the
squ
are
of a
nu
mbe
r�
11n
2
Wri
te a
ver
bal
exp
ress
ion
to
rep
rese
nt
each
eq
uat
ion
.7–
10.S
amp
le a
nsw
ers
7.n
�8
�16
8.8
�3x
�5
are
giv
en.
Th
e d
iffe
ren
ce o
f a
nu
mb
er
Th
e su
m o
f 8
and
3 t
imes
a
and
8 is
16.
nu
mb
er is
5.
9.b2
�3
�b
10.
�2
�2y
Th
ree
add
ed t
o t
he
squ
are
of
A n
um
ber
div
ided
by
3 is
th
ea
nu
mb
er is
th
e n
um
ber
.d
iffe
ren
ce o
f 2
and
tw
ice
the
nu
mb
er.
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch s
tate
men
t.
11.I
f a
�0.
5b,a
nd
0.5b
�10
,th
en a
�10
.12
.If
d�
1 �
f,th
en d
�f
�1.
Tran
siti
ve (
�)
Su
btr
acti
on
(�
)
13.I
f �
7x�
14,t
hen
14
��
7x.
14.I
f (8
�7)
r�
30,t
hen
15r
�30
.S
ymm
etri
c (�
)S
ub
stit
uti
on
(�
)
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
15.4
m�
2 �
184
16.x
�4
�5x
�2
17.3
t�
2t�
55
18.�
3b�
7 �
�15
�2b
19.�
5x�
3x�
243
20.4
v�
20 �
6 �
345
21.a
��
35
22.2
.2n
�0.
8n�
5 �
4n5
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
23.I
�pr
t,fo
r p
p�
24.y
�x
�12
,for
xx
�4y
�48
25.A
�,f
or y
y�
2A�
x26
.A�
2�r2
�2�
rh,f
or h
h�
A�
2r2
��
2r
x�
y
2
1 4I � rt
2a 5
22 � 5
1 � 2
y 33n � 9
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-3
Cha
pter
123
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Wri
te a
n a
lgeb
raic
exp
ress
ion
to
rep
rese
nt
each
ver
bal
exp
ress
ion
.
1.2
mor
e th
an t
he q
uoti
ent
of a
num
ber
and
52.
the
sum
of
two
con
secu
tive
in
tege
rs
�2
n�
(n�
1)
3.5
tim
es t
he
sum
of
a n
um
ber
and
14.
1 le
ss t
han
tw
ice
the
squ
are
of a
nu
mbe
r5(
m�
1)2y
2�
1
Wri
te a
ver
bal
exp
ress
ion
to
rep
rese
nt
each
eq
uat
ion
.5–
8.S
amp
le a
nsw
ers
5.5
�2x
�4
6.3y
�4y
3ar
e g
iven
.
Th
e d
iffe
ren
ce o
f 5
and
tw
ice
a T
hre
e ti
mes
a n
um
ber
is 4
tim
es
nu
mb
er is
4.
the
cub
e o
f th
e n
um
ber
.
7.3c
�2(
c�
1)8.
�3(
2m�
1)T
he
qu
oti
ent
Th
ree
tim
es a
nu
mb
er is
tw
ice
the
of
a n
um
ber
an
d 5
is 3
tim
es t
he
dif
fere
nce
of
the
nu
mb
er a
nd
1.
sum
of
twic
e th
e n
um
ber
an
d 1
.
Nam
e th
e p
rop
erty
ill
ust
rate
d b
y ea
ch s
tate
men
t.
9.If
t�
13 �
52,t
hen
52
�t
�13
.10
.If
8(2q
�1)
�4,
then
2(2
q�
1) �
1.S
ymm
etri
c (�
)D
ivis
ion
(�
)
11.I
f h
�12
�22
,th
en h
�10
.12
.If
4m�
�15
,th
en �
12m
�45
.S
ub
trac
tio
n (
�)
Mu
ltip
licat
ion
(�
)
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
on.
13.1
4 �
8 �
6r�
114
.9 �
4n�
�59
�17
15.
�n
�16
.s
��
17.�
1.6r
�5
��
7.8
818
.6x
�5
�7
�9x
19.5
(6 �
4v)
�v
�21
20.6
y�
5 �
�3(
2y�
1)
Sol
ve e
ach
eq
uat
ion
or
form
ula
for
th
e sp
ecif
ied
var
iab
le.
21.E
�m
c2,f
or m
m�
22.c
�,f
or d
d�
23.h
�vt
�gt
2 ,fo
r v
v�
24.E
�Iw
2�
U,f
or I
I�
Def
ine
a va
riab
le,w
rite
an
eq
uat
ion
,an
d s
olve
th
e p
rob
lem
.
25.G
EOM
ETRY
Th
e le
ngt
h o
f a
rect
angl
e is
tw
ice
the
wid
th.F
ind
the
wid
th i
f th
epe
rim
eter
is
60 c
enti
met
ers.
w�
wid
th;
2(2w
) �
2w�
60;
10 c
m
26.G
OLF
Lui
s an
d th
ree
frie
nds
wen
t go
lfin
g.T
wo
of t
he f
rien
ds r
ente
d cl
ubs
for
$6 e
ach.
The
tota
l cos
t of
the
ren
ted
club
s an
d th
e gr
een
fees
for
eac
h pe
rson
was
$76
.Wha
t w
as t
he c
ost
of t
he g
reen
fee
s fo
r ea
ch p
erso
n?g
�g
reen
fee
s p
er p
erso
n;6
(2)
�4g
�76
;$16
2(E
�U
)�
�w
21 2
h�
gt2
�t
3c�
1�
22d
�1
3
E � c2
1 � 63 � 7
4 � 5
1 � 511 12
3 45 6
1 � 45 8
1 23 4
m 5
y � 5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Prac
tice
S
olvi
ng
Eq
uat
ion
s
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A10
Chapter 1 A11 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-3)
Cha
pter
124
Gle
ncoe
Alg
ebra
2
1.A
GES
Rob
ert’s
fat
her
is
5 ye
ars
olde
rth
an 3
tim
es R
ober
t’s a
ge.L
et R
ober
t’sag
e be
den
oted
by
Ran
d le
t R
ober
t’sfa
ther
’s a
ge b
e de
not
ed b
y F
.Wri
te a
neq
uat
ion
th
at r
elat
es R
ober
t’s a
ge a
nd
his
fat
her
’s a
ge.
F �
3R�
5.
2.A
IRPL
AN
EST
he
nu
mbe
r of
pas
sen
gers
pan
d th
e n
um
ber
of s
uit
case
s s
that
an
airp
lan
e ca
n c
arry
are
rel
ated
by
the
equ
atio
n 1
80p
+ 60
s=
3,00
0.If
10
peop
le b
oard
th
e ai
rcra
ft,h
ow m
any
suit
case
s ca
n t
he
airp
lan
e ca
rry?
20 s
uit
case
s
3.G
EOM
ETRY
Th
e le
ngt
h o
f a
rect
angl
eis
10
un
its
lon
ger
than
its
wid
th.I
f th
e to
tal
peri
met
er o
f th
e re
ctan
gle
is
44 u
nit
s,w
hat
is
the
wid
th?
w �
6 u
nit
s
4.SA
VIN
GS
Jaso
n s
tart
ed w
ith
ddo
llar
s in
his
pig
gy b
ank.
On
e w
eek
late
r,Ja
son
dou
bled
th
e am
oun
t in
his
pig
gy b
ank.
An
oth
er w
eek
late
r,Ja
son
was
abl
e to
add
$20
to h
is p
iggy
ban
k.A
t th
is p
oin
t,th
epi
ggy
ban
k h
ad $
50 i
n i
t.W
hat
is
d?
15
DO
MIN
OES
For
Exe
rcis
es 5
an
d 6
,use
the
info
rmat
ion
bel
ow.
Nan
cy i
s se
ttin
g u
p a
trai
n o
f do
min
os f
rom
the
fron
t en
tran
ce s
trai
ght
dow
n t
he
hal
l to
the
kitc
hen
en
tran
ce.T
he
thic
knes
s of
eac
hdo
min
o is
t.N
ancy
pla
ces
the
dom
inoe
s so
that
th
at t
he
spac
e se
para
tin
g co
nse
cuti
vedo
min
oes
is 3
t.T
he
tota
l di
stan
ce t
hat
Ndo
min
oes
take
s u
p is
giv
en b
y d
= t(
4N+
1).
5.N
ancy
mea
sure
s h
er d
omin
oes
and
fin
dsth
at t
�1
cen
tim
eter
.Sh
e m
easu
res
the
dist
ance
of
her
hal
lway
an
d fi
nds
th
at
d�
321
cen
tim
eter
s.R
ewri
te t
he
equ
atio
n t
hat
rel
ates
d,t
,an
d N
wit
h t
he
give
n v
alu
es s
ubs
titu
ted
for
tan
d d
.32
1 �
4N�
1.
6.H
ow m
any
dom
inoe
s di
d N
ancy
hav
e in
her
hal
lway
?80
do
min
oes
3t
t
w
w �
10
Wor
d Pr
oble
m P
ract
ice
Sol
vin
g E
qu
atio
ns
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-3
Cha
pter
125
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Th
e G
ross
Nat
ion
al P
rodu
ct,G
NP,
is a
n i
mpo
rtan
t in
dica
tor
of U
.S.e
con
omy.
Th
e G
NP
con
tain
s in
form
atio
n a
bou
t th
e in
flat
ion
rat
e,th
e B
ond
mar
ket,
and
the
Sto
ck
mar
ket.
It i
s co
mpo
sed
of c
onsu
mer
goo
ds,i
nve
stm
ents
,gov
ern
men
t ex
pen
ditu
res,
expo
rts,
and
impo
rts.
Cal
cula
ted
from
GN
P �
C�
I�
G�
X�
M,w
her
e
Cis
con
sum
er g
oods
(e.
g.T
V’s
,Car
s,F
ood,
Fu
rnit
ure
,Clo
thes
,Doc
tors
’ fee
s,an
d D
inin
g)I
is i
nve
stm
ents
(e.
g.Fa
ctor
ies,
Com
pute
rs,A
irli
nes
,an
d H
ousi
ng)
Gis
gov
ern
men
t sp
endi
ng
and
inve
stm
ents
(e.
g.S
hip
s,R
oads
,Sch
ools
,NA
SA
,an
d B
ombs
)X
is e
xpor
ts (
e.g.
Cor
n,W
hea
t,C
ars,
and
Com
pute
rs)
Mis
for
im
port
s,(e
.g.C
ars,
Com
pute
r ch
ips,
Clo
thes
,an
d O
il)
1.T
he
mos
t im
port
ant
sect
or o
f th
e U
.S.e
con
omy
is c
onsu
mpt
ion
.It
mak
es u
p ab
out
60%
of
the
enti
re G
NP.
In 2
000,
the
U.S
.’s G
NP
was
10.
5 tr
illi
on d
olla
rs.I
n t
he
sam
eye
ar,t
her
e w
ere
1 tr
illi
on d
olla
rs i
n i
nve
stm
ents
,bu
t a
1 tr
illi
on d
olla
r tr
ade
defi
cit.
Ass
um
ing
that
con
sum
ptio
n m
ade
up
60%
of
the
GN
P,h
ow m
uch
did
th
e go
vern
men
tbu
dget
for
spe
ndi
ng?
10.5
�6.
3 �
1 �
G�
1.T
her
efo
re G
�4.
2 tr
illio
n d
olla
rs.
2.In
200
1,th
e U
.S.t
rade
def
icit
rem
ain
at
1 tr
illi
on d
olla
rs,i
nve
stm
ents
als
o re
mai
nst
eady
at
1 tr
illi
on d
olla
rs.H
owev
er c
onsu
mpt
ion
dip
ped
to o
nly
50%
of
the
GN
P,w
hic
h i
ncr
ease
d to
12
tril
lion
dol
lars
.Wh
at w
as t
he
effe
ct o
n g
over
nm
ent
spen
din
g?W
hat
mig
ht
hav
e ca
use
d th
e ch
ange
?G
over
nm
ent
spen
din
g m
ust
hav
e g
on
e u
p,i
n f
act
G�
6 tr
illio
n d
olla
rs.
Em
plo
ymen
t m
ay h
ave
cau
sed
a d
ip in
co
nsu
mp
tio
n.
3.If
th
e G
NP
rem
ain
s st
eady
,an
d so
do
inve
stm
ents
an
d go
vern
men
t sp
endi
ng,
but
the
trad
e de
fici
t in
crea
ses
(to
say
2 or
3 t
rill
ion
dol
lars
),w
hat
doe
s th
is s
ay a
bou
t th
eco
nsu
mpt
ion
lev
el?
Co
nsu
mp
tio
n w
ill in
crea
se.
4.D
eter
min
e if
th
ere
is a
tra
de s
urp
lus
or d
efic
it w
hen
th
ere
is 1
2 tr
illi
on d
olla
r G
NP,
2 tr
illi
on i
n i
nve
stm
ents
,3 t
rill
ion
in
gov
ern
men
t in
vest
men
ts,a
nd
5 tr
illi
on i
nco
nsu
mpt
ion
.Exp
lain
wh
y th
is s
itu
atio
n m
ay b
e fa
vora
ble.
Th
ere
is a
su
rplu
s.C
on
sum
pti
on
is r
edu
ced
,po
ssib
ly b
ecau
se t
he
cost
of
livin
g h
as r
edu
ced
.
Enri
chm
ent
Un
ited
Sta
tes’
Gro
ss N
atio
nal
Pro
du
ct
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A11
Chapter 1 A12 Glencoe Algebra 2
Answers (Lessons 1-3 and 1-4)
Gra
phin
g Ca
lcul
ator
Act
ivit
yS
olvi
ng
Eq
uat
ion
s an
d C
hec
kin
g S
olu
tion
s
Wh
en s
olvi
ng
equ
atio
ns,
chec
kin
g th
e so
luti
ons
is a
n i
mpo
rtan
t pr
oces
s.A
grap
hin
g ca
lcu
lato
r ca
n b
e u
sed
to c
hec
k th
e so
luti
on o
f an
equ
atio
n.
Sol
ve�
2(5y
�1)
�y
��
4(y
�3)
.
Gra
ph t
he
expr
essi
on o
n t
he
left
sid
e of
th
e eq
uat
ion
in
Y1
and
the
expr
essi
on o
n t
he
righ
t si
de o
f th
e eq
uat
ion
in
Y2.
Ch
oose
an
appr
opri
ate
view
win
dow
so
that
th
e in
ters
ecti
on o
f th
e gr
aph
s is
visi
ble.
Th
en u
se t
he
inte
rsec
t co
mm
and
to f
ind
the
coor
din
ates
of
the
com
mon
poi
nt.
Key
stro
kes:
2 5
1 4
3 6
8 [C
AL
C]
5 [Q
UIT
] .
The
x-c
oord
inat
e,��
710 �,i
s th
e so
luti
on t
o th
e eq
uati
on.T
he y
-coo
rdin
ate
is t
he
valu
e of
bot
h s
ides
of
the
equ
atio
n w
hen
x�
��710 �
.
EN
TER
EN
TER
MA
TH
2nd
EN
TER
EN
TER
EN
TER
2nd
EN
TER
ZO
OM
ZO
OM
)—
(
(–)
EN
TER
—)
—(
(–)
Y=
Sol
ve e
ach
eq
uat
ion
.
1.�
3(2w
�7)
�9
�2(
5w�
4)2.
1.5(
4 �
x) �
1.3(
2 �
x)3.
�1 4�(a
�2)
��1 6�(
5 �
a)
w�
��5 2�
x�
17a
��4 5�
4.3(
2z�
25)
�2(
z�
1) �
785.
�m3�
4�
��3m
5�1
��
16.
�x� 2
5�
��1 2�
�2x
��x
� 83
�
z�
�1 4�m
��
8x
��2 11 1�
Sol
ve �x 5�
��x 4�
��1 2�(
x�
2).
Gra
ph t
he
expr
essi
on o
n t
he
left
sid
e of
th
e eq
uat
ion
in
Y1
and
the
expr
essi
on o
n t
he
righ
t si
de o
f th
e eq
uat
ion
in
Y2.
En
ter
Y1
- Y
2in
Y3.
Th
en g
raph
th
e fu
nct
ion
in
Y3.
Use
th
e ze
ro f
un
ctio
n u
nde
r th
eC
AL
Cm
enu
to
dete
rmin
e w
her
e th
e gr
aph
of
Y3
equ
als
zero
.Th
ispo
int
wil
l be
th
e so
luti
on.
Key
stro
kes:
5 4
1 2
2 2
6 [C
AL
C]
2.
Use
arr
ow k
eys
and
ente
r to
set
th
e bo
un
d pr
ompt
s.T
he
solu
tion
is
x�
�2 10 1�.
2nd
ZO
OM
EN
TER
EN
TER
EN
TER
VA
RS
—E
NTE
RE
NTE
R
VA
RS
EN
TER
)—
()
�(
EN
TER
)�
(—
)�
(Y
=
[�47
, 47]
scl
:10
by [�
31, 3
1] s
cl:1
0
[�10
, 10]
scl
:1 b
y [�
10, 1
0] s
cl:1
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-3
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
1
Exam
ple
2
Cha
pter
126
Gle
ncoe
Alg
ebra
2
Exer
cise
s
Lesson 1-4
Cha
pter
127
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-4 i
n y
our
text
boo
k.
•W
hat
is
a se
ism
olog
ist
and
wh
at d
oes
mag
nit
ude
of
an e
arth
quak
e m
ean
?a
scie
nti
stw
ho
stu
die
s ea
rth
qu
akes
;a
nu
mb
er f
rom
1 t
o 1
0 th
at t
ells
ho
w s
tro
ng
an
eart
hq
uak
e is
•W
hy
is a
n a
bsol
ute
val
ue
equ
atio
n r
ath
er t
han
an
equ
atio
n w
ith
out
abso
lute
val
ue
use
dto
fin
d th
e ex
trem
es i
n t
he
actu
al m
agn
itu
de o
f an
ear
thqu
ake
in r
elat
ion
to
its
mea
sure
dva
lue
on t
he
Ric
hte
r sc
ale?
Sam
ple
an
swer
:Th
e ac
tual
mag
nit
ud
e ca
n v
ary
fro
m t
he
mea
sure
d m
agn
itu
de
by u
p t
o 0
.3 u
nit
in e
ith
er d
irec
tio
n,s
o a
nab
solu
te v
alu
e eq
uat
ion
is n
eed
ed.
•If
th
e m
agn
itu
de o
f an
ear
thqu
ake
is e
stim
ated
to
be 6
.9 o
n t
he
Ric
hte
r sc
ale,
it m
igh
tac
tual
ly h
ave
a m
agn
itu
de a
s lo
w a
s or
as
hig
h a
s .
Rea
d t
he
Less
on
1.E
xpla
in h
ow �
aco
uld
rep
rese
nt
a po
siti
ve n
um
ber.
Giv
e an
exa
mpl
e.S
amp
lean
swer
:If
ais
neg
ativ
e,th
en �
ais
po
siti
ve.E
xam
ple
:If
a�
�25
,th
en
�a
��
(�25
) �
25.
2.E
xpla
in w
hy
the
abso
lute
val
ue
of a
nu
mbe
r ca
n n
ever
be
neg
ativ
e.S
amp
le a
nsw
er:
Th
e ab
solu
te v
alu
e is
th
e n
um
ber
of
un
its
it is
fro
m 0
on
th
e n
um
ber
lin
e.T
he
nu
mb
er o
f u
nit
s is
nev
er n
egat
ive.
3.W
hat
doe
s th
e se
nte
nce
b�
0 m
ean
?S
amp
le a
nsw
er:T
he
nu
mb
er b
is 0
or
gre
ater
th
an 0
.
4.W
hat
doe
s th
e sy
mbo
l �
mea
n a
s a
solu
tion
set
?S
amp
le a
nsw
er:
If a
so
luti
on
set
is �
,th
en t
her
e ar
e n
o s
olu
tio
ns.
Rem
emb
er W
hat
Yo
u L
earn
ed
5.H
ow c
an t
he
nu
mbe
r li
ne
mod
el f
or a
bsol
ute
val
ue
that
is
show
n o
n p
age
28 o
f yo
ur
text
book
hel
p yo
u r
emem
ber
that
man
y ab
solu
te v
alu
e eq
uat
ion
s h
ave
two
solu
tion
s?S
amp
le a
nsw
er:T
he
nu
mb
er li
ne
sho
ws
that
fo
r ev
ery
po
siti
ve n
um
ber
,th
ere
are
two
nu
mb
ers
that
hav
e th
at n
um
ber
as
thei
r ab
solu
te v
alu
e.
7.2
6.6
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-4
Less
on R
eadi
ng G
uide
Sol
vin
g A
bso
lute
Val
ue
Eq
uat
ion
s
A1-A23 A2-01-873971 5/25/06 2:55 PM Page A12
Chapter 1 A13 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-4)
Ab
solu
te V
alu
e Ex
pre
ssio
ns
Th
e ab
solu
te v
alu
eof
a n
um
ber
is t
he
nu
mbe
r of
un
its
it i
s fr
om 0
on
a n
um
ber
lin
e.T
he
sym
bol
⏐x⏐
is u
sed
to r
epre
sen
t th
e ab
solu
te v
alu
eof
a n
um
ber
x.
•W
ord
sF
or a
ny r
eal n
umbe
r a
, if
ais
pos
itive
or
zero
, th
e ab
solu
te v
alue
of
ais
a.
Ab
solu
te V
alu
eIf
ais
neg
ativ
e, t
he a
bsol
ute
valu
e of
ais
the
opp
osite
of
a.
•S
ymb
ols
For
any
rea
l num
ber
a,
⏐a⏐
�a,
if a
0,
and
⏐a ⏐
��
a, if
a�
0.
Eva
luat
e � �
4�
�� �
2x�
ifx
�6.
⏐�4⏐
�⏐�
2x⏐
�⏐�
4⏐�
⏐�2
6⏐
�⏐�
4⏐�
⏐�12
⏐�
4 �
12�
�8
Eva
luat
e ea
ch e
xpre
ssio
n i
f w
��
4,x
�2,
y�
,an
d z
��
6.
1.⏐2
x�
8⏐4
2.⏐6
�z⏐
�⏐�
7⏐�
73.
5 �
⏐w�
z⏐15
4.⏐x
�5⏐
�⏐2
w⏐
�1
5.⏐x
⏐�
⏐y⏐
�⏐z
⏐�
46.
⏐7 �
x⏐�
⏐3x⏐
11
7.⏐w
�4x
⏐12
8.⏐w
z⏐�
⏐xy⏐
239.
⏐z⏐
�3⏐
5yz⏐
�39
10.5
⏐w⏐
�2⏐
z�
2y⏐
3411
.⏐z⏐
�4⏐
2z�
y⏐�
4012
.10
�⏐x
w⏐
2
13.⏐
6y�
z⏐�
⏐yz⏐
614
.3⏐w
x⏐�
⏐4x
�8y
⏐27
15.7
⏐yz⏐
�30
�9
16.1
4 �
2⏐w
�xy
⏐4
17.⏐
2x�
y⏐�
5y6
18.⏐
xyz⏐
�⏐w
xz⏐
54
19.z
⏐z⏐
�x⏐
x⏐�
3220
.12
�⏐1
0x�
10y⏐
�3
21.
⏐5z
�8w
⏐31
22.⏐
yz�
4w⏐
� w
1723
.⏐w
z⏐�
⏐8y⏐
2024
.xz
�⏐x
z⏐�
241 2
3 4
1 2
1 4
1 � 2
1 � 2
Stud
y G
uide
and
Inte
rven
tion
Sol
vin
g A
bso
lute
Val
ue
Eq
uat
ion
s
Eva
luat
e � 2
x�
3y�
if
x�
�4
and
y�
3.
⏐2x
�3y
⏐�
⏐2(�
4) �
3(3)
⏐�
⏐�8
�9⏐
�⏐�
17⏐
�17
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-4
Cha
pter
128
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1Ex
ampl
e 2
Exer
cise
s
Lesson 1-4
Cha
pter
129
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Ab
solu
te V
alu
e Eq
uat
ion
sU
se t
he
defi
nit
ion
of
abso
lute
val
ue
to s
olve
equ
atio
ns
con
tain
ing
abso
lute
val
ue
expr
essi
ons.
For
any
rea
l num
bers
aan
d b,
whe
re b
0,
if ⏐
a⏐�
bth
en a
�b
or a
��
b.
Alw
ays
chec
k yo
ur
answ
ers
by s
ubs
titu
tin
g th
em i
nto
th
e or
igin
al e
quat
ion
.Som
etim
esco
mpu
ted
solu
tion
s ar
e n
ot a
ctu
al s
olu
tion
s.
Sol
ve
� 2x
�3
� �
17.C
hec
k y
our
solu
tion
s.
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Sol
vin
g A
bso
lute
Val
ue
Eq
uat
ion
s
Cas
e 1
a�
b2x
�3
�17
2x�
3 �
3 �
17 �
32x
�20
x�
10
CH
ECK
⏐2x
�3⏐
�17
⏐2(1
0) �
3⏐�
17⏐2
0 �
3⏐�
17⏐1
7⏐�
1717
�17
✓
Cas
e 2
a�
�b
2x�
3 �
�17
2x�
3 �
3 �
�17
�3
2x�
�14
x�
�7
CH
ECK
⏐2(�
7) �
3⏐�
17⏐�
14 �
3⏐�
17⏐�
17⏐
�17
17 �
17 ✓
Th
ere
are
two
solu
tion
s,10
an
d �
7.
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
1.⏐x
�15
⏐�
37
{�52
,22}
2.⏐t
�4⏐
�5
�0
{�1,
9}
3.⏐x
�5⏐
�45
{�
40,5
0}4.
⏐m�
3⏐�
12 �
2m{3
}
5.⏐5
b�
9⏐�
16 �
2�
6.⏐1
5 �
2k⏐
�45
{�15
,30}
7.5n
�24
�⏐8
�3n
⏐{�
2}8.
⏐8 �
5a⏐
�14
�a
��,1
�9.
⏐4p
�11
⏐�
p�
4�23
,��
10.⏐
3x�
1⏐�
2x�
11{�
2,12
}
11. ⏐
x�
3 ⏐��
1�
12.4
0 �
4x�
2⏐3x
�10
⏐{6
,�10
}
13.5
f�
⏐3f
�4⏐
�20
{12}
14.⏐
4b�
3⏐�
15 �
2b{2
,�9}
15.
⏐6 �
2x⏐
�3x
�1
��
16.⏐
16 �
3x⏐
�4x
�12
{4}
1 � 21 2
1 3
1 � 71 3
11 � 2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-4
Exam
ple
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A13
Chapter 1 A14 Glencoe Algebra 2
Answers (Lesson 1-4)
Cha
pter
130
Gle
ncoe
Alg
ebra
2
Skill
s Pr
acti
ceS
olvi
ng
Ab
solu
te V
alu
e E
qu
atio
ns
Eva
luat
e ea
ch e
xpre
ssio
n i
f w
�0.
4,x
�2,
y�
�3,
and
z�
�10
.
1.⏐5
w⏐
22.
⏐�9y
⏐27
3.⏐9
y�
z⏐17
4.�
⏐17z
⏐�
170
5.�
⏐10z
�31
⏐�
131
6.�
⏐8x
�3y
⏐�
⏐2y
�5x
⏐�
21
7.25
�⏐5
z�
1⏐�
248.
44 �
⏐�2x
�y⏐
45
9.2⏐
4w⏐
3.2
10.3
�⏐1
�6w
⏐1.
6
11.⏐
�3x
�2y
⏐�
4�
412
.6.4
�⏐w
�1⏐
7
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
13.⏐
y�
3⏐�
2{�
5,�
1}14
.⏐5a
⏐�
10{�
2,2}
15.⏐
3k�
6⏐�
2�
,�
16.⏐
2g�
6⏐�
0{�
3}
17.1
0 �
⏐1 �
c⏐{�
9,11
}18
.⏐2x
�x⏐
�9
{�3,
3}
19.⏐
p�
7⏐�
�14
�20
.2⏐3
w⏐
�12
{�2,
2}
21.⏐
7x�
3x⏐
�2
�18
{�4,
4}22
.4⏐7
�y⏐
�1
�11
{4,1
0}
23.⏐
3n�
2⏐�
�,
�24
.⏐8d
�4d
⏐�
5 �
13{�
2,2}
25.�
5⏐6a
�2⏐
��
15��
,�
26.⏐
k⏐�
10 �
9�
1 � 65 � 6
5 � 61 � 2
1 2
8 � 34 � 3
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Eva
luat
e ea
ch e
xpre
ssio
n i
f a
��
1,b
��
8,c
�5,
and
d�
�1.
4.
1.⏐6
a⏐6
2.⏐2
b�
4⏐12
3.�
⏐10d
�a⏐
�15
4.⏐1
7c⏐
�⏐3
b�
5⏐11
4
5.�
6⏐10
a�
12⏐
�13
26.
⏐2b
�1⏐
�⏐�
8b�
5⏐�
52
7.⏐5
a�
7⏐�
⏐3c
�4⏐
238.
⏐1 �
7c⏐
�⏐a
⏐33
9.�
3⏐0.
5c�
2⏐�
⏐�0.
5b⏐
�17
.510
.⏐4d
⏐�
⏐5 �
2a⏐
12.6
11.⏐
a�
b⏐�
⏐b�
a⏐14
12.⏐
2 �
2d⏐
�3⏐
b⏐�
19.2
Sol
ve e
ach
eq
uat
ion
.Ch
eck
you
r so
luti
ons.
13.⏐
n�
4⏐�
13{�
9,17
}14
.⏐x
�13
⏐�
2{1
1,15
}
15.⏐
2y�
3⏐�
29{�
13,1
6}16
.7⏐x
�3⏐
�42
{�9,
3}
17.⏐
3u�
6⏐�
42{�
12,1
6}18
.⏐5x
�4⏐
��
6�
19.�
3⏐4x
�9⏐
�24
�20
.�6⏐
5 �
2y⏐
��
9�1.
75,3
.25 �
21.⏐
8 �
p⏐�
2p�
3{1
1}22
.⏐4w
�1⏐
�5w
�37
{�38
}
23.4
⏐2y
�7⏐
�5
�9
{3,4
}24
.�2⏐
7 �
3y⏐
�6
��
14�1,
3�
25.2
⏐4 �
s⏐�
�3s
{�8}
26.5
�3⏐
2 �
2w⏐
��
7{�
3,1}
27.5
⏐2r
�3⏐
�5
�0
{�2,
�1}
28.3
�5⏐
2d�
3⏐�
4�
29.W
EATH
ERA
th
erm
omet
er c
omes
wit
h a
gu
aran
tee
that
th
e st
ated
tem
pera
ture
dif
fers
from
th
e ac
tual
tem
pera
ture
by
no
mor
e th
an 1
.5 d
egre
es F
ahre
nh
eit.
Wri
te a
nd
solv
e an
equ
atio
n t
o fi
nd
the
min
imu
m a
nd
max
imu
m a
ctu
al t
empe
ratu
res
wh
en t
he
ther
mom
eter
sta
tes
that
th
e te
mpe
ratu
re i
s 87
.4 d
egre
es F
ahre
nh
eit.
� x�
87.4
� �
1.5;
or
85.9
�x
� 8
8.9
30.O
PIN
ION
PO
LLS
Pu
blic
opi
nio
n p
olls
rep
orte
d in
new
spap
ers
are
usu
ally
giv
en w
ith
am
argi
n o
f er
ror.
For
exa
mpl
e,a
poll
wit
h a
mar
gin
of
erro
r of
�5%
is
con
side
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accu
rate
to w
ith
in p
lus
or m
inu
s 5%
of
the
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al v
alu
e.A
pol
l w
ith
a s
tate
d m
argi
n o
f er
ror
of�
3% p
redi
cts
that
can
dida
te T
onw
e w
ill
rece
ive
51%
of
an u
pcom
ing
vote
.Wri
te a
nd
solv
e an
equ
atio
n d
escr
ibin
g th
e m
inim
um
an
d m
axim
um
per
cen
t of
th
e vo
te t
hat
can
dida
te T
onw
e is
exp
ecte
d to
rec
eive
.� x
�51
� �
3 o
r 48
�x
� 5
4
2 � 3
Prac
tice
Sol
vin
g A
bso
lute
Val
ue
Eq
uat
ion
s
Lesson 1-4
Cha
pter
131
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-4
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A14
Chapter 1 A15 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-4)
Cha
pter
132
Gle
ncoe
Alg
ebra
2
1.LO
CA
TIO
NS
Iden
tica
l va
cati
onco
ttag
es,e
qual
ly s
pace
d al
ong
a st
reet
,ar
e n
um
bere
d co
nse
cuti
vely
beg
inn
ing
wit
h 1
0.M
aria
liv
es i
n c
otta
ge #
17.
Josh
ua
live
s 4
cott
ages
aw
ay f
rom
Mar
ia.I
f n
repr
esen
ts J
osh
ua’
s co
ttag
en
um
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�17
| �
4.W
hat
are
the
poss
ible
nu
mbe
rs o
f Jo
shu
a’s
cott
age?
13 o
r 21
2.H
EIG
HT
Sar
ah a
nd
Jess
ica
are
sist
ers.
Sar
ah’s
hei
ght
is s
inch
es a
nd
Jess
ica’
sh
eigh
t is
jin
ches
.Th
eir
fath
er w
ants
to
kn
ow h
ow m
any
inch
es s
epar
ate
the
two.
Wri
te a
n e
quat
ion
for
th
isdi
ffer
ence
in
su
ch a
way
th
at t
he
resu
ltw
ill
alw
ays
be p
osit
ive
no
mat
ter
wh
ich
sist
er i
s ta
ller
.d
�|s
�j|
or
d �
|j�
s|
3.A
GES
Rh
onda
con
duct
s a
surv
ey o
f th
eag
es o
f st
ude
nts
in
ele
ven
th g
rade
at
her
sch
ool.
On
Nov
embe
r 1,
she
fin
ds t
he
aver
age
age
is 2
00 m
onth
s.S
he
also
fin
ds t
hat
tw
o-th
irds
of
the
stu
den
ts
are
wit
hin
3 m
onth
s of
th
e av
erag
e ag
e.W
rite
an
d so
lve
an e
quat
ion
to
dete
rmin
e th
e ag
e li
mit
s fo
r th
is g
rou
pof
stu
den
ts.
|a�
200|
�3
a�
197
or
203
4.TO
LER
AN
CE
Mar
tin
mak
es e
xerc
ise
wei
ghts
.For
his
10
pou
nd
dum
bbel
ls,h
egu
aran
tees
th
at t
he
actu
al w
eigh
t of
his
dum
bbel
ls i
s w
ith
in 0
.1 p
oun
ds o
f 10
pou
nds
.Wri
te a
nd
solv
e an
equ
atio
n t
hat
desc
ribe
s th
e m
inim
um
an
d m
axim
um
wei
ght
of h
is 1
0 po
un
d du
mbb
ells
.| w
�10
| �0.
1m
inim
um
wei
gh
t:9.
9 p
ou
nd
sm
axim
um
wei
gh
t:10
.1 p
ou
nd
s
WA
LKIN
GF
or E
xerc
ises
5–7
,use
th
efo
llow
ing
info
rmat
ion
.
Jim
is
wal
kin
g al
ong
a st
raig
ht
lin
e.A
nob
serv
er w
atch
es h
im.I
f Ji
m w
alks
for
war
d,th
e ob
serv
er r
ecor
ds t
he
dist
ance
as
apo
siti
ve n
um
ber,
but
if h
e w
alks
bac
kwar
d,th
e ob
serv
er r
ecor
ds t
he
dist
ance
as
an
egat
ive
nu
mbe
r.T
he
obse
rver
has
rec
orde
dth
at J
im h
as w
alke
d a,
then
b,t
hen
cfe
et.
5.W
rite
a f
orm
ula
for
th
e to
tal
dist
ance
that
Jim
wal
ked.
T�
|a|
�|b
|�
|c|
6.T
he
equ
atio
n y
ou w
rote
in
par
t A
sh
ould
not
be
T�
|a�
b�
c|.
Wh
at d
oes
|a�
b�
c| r
epre
sen
t?T
he
dis
tan
ce J
im e
nd
s u
p f
rom
wh
ere
he
star
ted
.
7.W
hen
wou
ld t
he
form
ula
you
wro
te i
npa
rt A
giv
e th
e sa
me
valu
e as
th
e fo
rmu
lash
own
in
par
t B
?T
hey
will
be
equ
al o
nly
if J
im w
alks
in t
he
sam
e d
irec
tio
n e
ach
tim
e g
ivin
g a
,b,a
nd
cal
l th
e sa
me
sig
n.
1012
1416
1820
2422
Mar
ia’s
Wor
d Pr
oble
m P
ract
ice
Sol
vin
g A
bso
lute
Val
ue
Eq
uat
ion
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-5
Cha
pter
133
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Con
sid
erin
g A
ll C
ases
in A
bso
lute
Val
ue
Eq
uat
ion
s Yo
u h
ave
lear
ned
th
at a
bsol
ute
val
ue
equ
atio
ns
wit
h o
ne
set
of a
bsol
ute
val
ue
sym
bols
hav
e tw
o ca
ses
that
mu
st b
e co
nsi
dere
d.F
or e
xam
ple,
|x�
3|�
5 m
ust
be b
roke
n i
nto
x�
3 �
5 or
�(x
�3)
�5.
For
an
equ
atio
n w
ith
tw
o se
ts o
fab
solu
te v
alu
e sy
mbo
ls,f
our
case
s m
ust
be
con
side
red.
Con
side
r th
e pr
oble
m |x
�2
|�3
�|x
�6
|.Fir
st w
e m
ust
wri
te t
he
equ
atio
ns
for
the
case
wh
ere
x�
6
0 an
d w
her
ex
�6
�0.
Her
e ar
e th
e eq
uat
ion
s fo
rth
ese
two
case
s:
|x�
2|�
3 �
x�
6
|x�
2|�
3 �
�(x
�6)
Eac
h o
f th
ese
equ
atio
ns
also
has
tw
o ca
ses.
By
wri
tin
g th
e eq
uat
ion
s fo
r bo
thca
ses
of e
ach
equ
atio
n a
bove
,you
en
d u
p w
ith
th
e fo
llow
ing
fou
r eq
uat
ion
s:
x�
2 �
3 �
x�
6x
�2
�3
��
(x�
6)
�(x
�2)
�3
�x
�6
�x
�2
�3
��
(x�
6)
Sol
ve e
ach
of
thes
e eq
uat
ion
s an
d ch
eck
you
r so
luti
ons
in t
he
orig
inal
equ
atio
n,
|x�
2|�
3 �
|x�
6|.T
he
only
sol
uti
on t
o th
is e
quat
ion
is
�5 2 .
Sol
ve e
ach
ab
solu
te v
alu
e eq
uat
ion
.Ch
eck
you
r so
luti
on.
1.|x
�4
|�|x
�7
|x�
�1.
52.
|2x�
9|�
|x�
3|x
��
12,�
2
3.|�
3x�
6|�
|5x�
10|x
��
24.
|x�
4|�
6 �
|x�
3|x
�2.
5
5.H
ow m
any
case
s w
ould
th
ere
be f
or a
n a
bsol
ute
val
ue
equ
atio
n c
onta
inin
g th
ree
sets
of
abso
lute
val
ue
sym
bols
?8
6.L
ist
each
cas
e an
d so
lve
|x�
2|�
|2x
�4
|�|x
�3
|.Ch
eck
you
r so
luti
on.
x�
2 �
2x�
4 �
x�
3 �
(x�
2) �
2x�
4 �
x�
3
x�
2 �
2x�
4 �
�(x
�3)
�
(x�
2) �
2x�
4 �
�(x
�3)
�(x
�2)
�(�
2x�
4) �
x�
3x
�2
�(�
2x�
4) �
x�
3
�(x
�2)
�(�
2x�
4) �
�(x
�3)
x�
2 �
(�2x
�4)
��
(x�
3)
no
so
luti
on
Enri
chm
ent
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
Exer
cise
s
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A15
Chapter 1 A16 Glencoe Algebra 2
Answers (Lessons 1-4 and 1-5)
Cha
pter
134
Gle
ncoe
Alg
ebra
2
You
can
use
a s
prea
dsh
eet
to t
ry s
ever
al d
iffe
ren
t va
lues
in
an
equ
atio
n t
oh
elp
you
det
erm
ine
wh
eth
er t
he
stat
emen
t is
som
etim
es,a
lway
s,or
nev
ertr
ue.
Rem
embe
r th
at s
how
ing
that
a s
tate
men
t is
tru
e fo
r so
me
valu
es d
oes
not
pro
ve t
hat
it
is t
rue
for
all
valu
es.H
owev
er,f
indi
ng
one
valu
e fo
r w
hic
h a
stat
emen
t is
fal
se p
rove
s th
at i
t is
not
tru
e fo
r al
l va
lues
.
Spre
adsh
eet
Act
ivit
yA
bso
lute
Val
ue
Sta
tem
ents
Use
a s
pre
adsh
eet
to d
eter
min
e w
het
her
eac
h a
bso
lute
val
ue
stat
emen
t is
som
etim
es,a
lwa
ys,o
r n
ever
tru
e.
1.F
or a
ll r
eal
nu
mbe
rs a
and
b,a
�0,
|ax
�b|
�0.
som
etim
es
2.If
aan
d b
are
real
nu
mbe
rs,t
hen
|a
�b|
�|a
| �
|b|.
som
etim
es
3.If
aan
d b
are
real
nu
mbe
rs,t
hen
|a
�b|
��
x.n
ever
4.If
aan
d b
are
real
nu
mbe
rs,t
hen
|a|
�|b
| �
a�
b.so
met
imes
5.If
aan
d b
are
real
nu
mbe
rs,t
hen
c|a
�b|
�c|
a|�
|b|.
som
etim
es
Det
erm
ine
wh
eth
er c
|a�
b|�
|ca
�cb
| is
som
etim
es,a
lwa
ys,o
rn
ever
tru
e.T
ry a
nu
mbe
r of
val
ues
for
a,b
,an
d c
to d
eter
min
e w
het
her
th
e st
atem
ent
istr
ue
or f
alse
for
eac
h s
et o
f va
lues
.
Ste
p1
Use
Col
um
ns
A,B
,an
d C
for
the
valu
es o
f a,
b,an
dc.
Ch
oose
sev
eral
set
s of
valu
es i
ncl
udi
ng
posi
tive
and
neg
ativ
e n
um
bers
,an
d ze
ro.
Ste
p2
Use
Col
um
n D
to
test
the
equ
atio
n.A
for
mu
lasu
ch a
s C
2*A
BS
(A2�
B2)
�A
BS
(C2*
A2�
C2*
B2)
in c
ell
D2
retu
rns
TR
UE
if t
he
equ
atio
n i
s tr
ue.
Th
rou
gh o
bser
vati
on o
f C
olu
mn
D,w
hen
cis
neg
ativ
e th
e st
atem
ent
is n
ottr
ue.
Th
e ab
solu
te v
alu
e st
atem
ent,
c|a
�b|
�|c
a�
cb|
is s
omet
imes
tru
e;it
is
tru
e on
ly i
f c
0.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-4
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Less
on R
eadi
ng G
uide
Sol
vin
g I
neq
ual
itie
s
Lesson 1-5
Cha
pter
135
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-5 i
n y
our
text
boo
k.
•W
rite
an
in
equ
alit
y co
mpa
rin
g th
e n
um
ber
of m
inu
tes
per
mon
th i
ncl
ude
d in
th
e tw
oph
one
plan
s.15
0
400
or
400
�15
0•
Su
ppos
e th
at i
n o
ne
mon
th y
ou u
se 4
75 m
inu
tes
of a
irti
me
on y
our
wir
eles
s ph
one.
Fin
dyo
ur
mon
thly
cos
t w
ith
eac
h p
lan
.
Pla
n 1
:P
lan
2:
Wh
ich
pla
n s
hou
ld y
ou c
hoo
se?
Rea
d t
he
Less
on
1.T
her
e ar
e se
vera
l di
ffer
ent
way
s to
wri
te o
r sh
ow i
neq
ual
itie
s.W
rite
eac
h o
f th
efo
llow
ing
in i
nte
rval
not
atio
n.
a.{x
� x,�
3}
b.
{x� x
�5}
c.{x
� x�
2}
d.
{x� x
� �
1}
2.S
how
how
you
can
wri
te a
n i
neq
ual
ity
sym
bol
foll
owed
by
a n
um
ber
to d
escr
ibe
each
of
the
foll
owin
g si
tuat
ion
s.
a.T
her
e ar
e fe
wer
th
an 6
00 s
tude
nts
in
th
e se
nio
r cl
ass.
60
0
b.
A s
tude
nt
may
en
roll
in
no
mor
e th
an s
ix c
ours
es e
ach
sem
este
r.�
6
c.To
par
tici
pate
in
a co
ncer
t,yo
u m
ust
be w
illi
ng t
o at
tend
at
leas
t te
n re
hear
sals
.�
10
d.
Th
ere
is s
pace
for
at
mos
t 16
5 st
ude
nts
in
th
e h
igh
sch
ool
ban
d.�
165
Rem
emb
er W
hat
Yo
u L
earn
ed
3.O
ne
way
to
rem
embe
r so
met
hin
g is
to
expl
ain
it
to a
not
her
per
son
.A c
omm
on s
tude
nt
erro
r in
sol
vin
g in
equ
alit
ies
is f
orge
ttin
g to
rev
erse
th
e in
equ
alit
y sy
mbo
l w
hen
mu
ltip
lyin
g or
div
idin
g bo
th s
ides
of
an i
neq
ual
ity
by a
neg
ativ
e n
um
ber.
Su
ppos
e th
atyo
ur
clas
smat
e is
hav
ing
trou
ble
rem
embe
rin
g th
is r
ule
.How
cou
ld y
ou e
xpla
in t
his
ru
leto
you
r cl
assm
ate?
Sam
ple
an
swer
:D
raw
a n
um
ber
lin
e.P
lot
two
po
siti
ven
um
ber
s,fo
r ex
amp
le,3
an
d 8
.Th
en p
lot
thei
r ad
dit
ive
inve
rses
,�3
and
�8.
Wri
te a
n in
equ
alit
y th
at c
om
par
es t
he
po
siti
ve n
um
ber
s an
d o
ne
that
com
par
es t
he
neg
ativ
e n
um
ber
s.N
oti
ce t
hat
8 �
3,bu
t �
8
�3.
Th
eo
rder
ch
ang
es w
hen
yo
u m
ult
iply
by
�1.
32
54
10
�1
�2
�3
�4
�5
�5
�4
�3
�2
�1
01
23
45
76
98
54
32
1�
0�
1�5
�4
�3
�2
�1
01
23
45
Pla
n 2
$55
$65
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A16
Chapter 1 A17 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-5)
Cha
pter
136
Gle
ncoe
Alg
ebra
2
Stud
y G
uide
and
Inte
rven
tion
Sol
vin
g I
neq
ual
itie
s
Solv
e In
equ
alit
ies
Th
e fo
llow
ing
prop
erti
es c
an b
e u
sed
to s
olve
in
equ
alit
ies.
Ad
dit
ion
an
d S
ub
trac
tio
n P
rop
erti
es f
or
Ineq
ual
itie
sM
ult
iplic
atio
n a
nd
Div
isio
n P
rop
erti
es f
or
Ineq
ual
itie
s
For
any
rea
l num
bers
a,
b, a
nd c
:F
or a
ny r
eal n
umbe
rs a
, b,
and
c,
with
c�
0:1.
If a
�b,
the
n a
�c
�b
�c
and
a�
c�
b�
c.1.
If c
is p
ositi
ve a
nd a
�b,
the
n ac
�bc
and
�.
2.If
a�
b, t
hen
a�
c�
b�
can
d a
�c
�b
�c.
2.If
cis
pos
itive
and
a�
b, t
hen
ac�
bcan
d �
.
3.If
cis
neg
ativ
e an
d a
�b,
the
n ac
�bc
and
�.
4.If
cis
neg
ativ
e an
d a
�b,
the
n ac
�bc
and
�.
Th
ese
prop
erti
es a
re a
lso
tru
e fo
r �
and
.
b ca c
b ca c
b ca c
b ca c
Sol
ve 1
7 �
3w�
35.T
hen
grap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
17 �
3w
3517
�3w
�17
35
�17
�3w
18
w�
�6
Th
e so
luti
on s
et i
s {w
⏐w �
�6}
.
�9
�8
�7
�6
�5
�4
�3
�2
�1
Sol
ve 2
x�
4 �
36.
Th
en g
rap
h t
he
solu
tion
set
on
an
um
ber
lin
e.
2x�
4 �
4 �
36 �
42x
�32
x�
16T
he
solu
tion
set
is
{x⏐x
�16
}.
2120
1918
1716
1514
13
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er n
otat
ion
.T
hen
gra
ph
th
e so
luti
on s
et o
n a
nu
mb
er l
ine.
1.7(
7a�
9) �
842.
3(9z
�4)
�35
z�
43.
5(12
�3n
) �
165
{a� a
�3}
{z
� z
2}{n
� n�
�7}
4.18
�4k
�2(
k�
21)
5.4(
b�
7) �
6 �
226.
2 �
3(m
�5)
4(
m�
3)
{k� k
��
4}{b
� b
11}
{m� m
�5}
7.4x
�2
��
7(4x
�2)
8.(2
y�
3) �
y�
29.
2.5d
�15
�75
�x� x
��
{y� y
�
9}
{d� d
�24
}
2122
1920
2324
2526
27�
12�
14�
10�
8�
6�
4�
3�
2�
10
12
34
1 � 2
1 3
23
01
45
67
88
96
710
1112
1314
�8
�7
�6
�5
�4
�3
�2
�1
0
�8
�7
�6
�5
�4
�3
�2
�1
0�
2�
1�
4�
30
12
34
�2
�1
�4
�3
01
23
4
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1Ex
ampl
e 2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Cha
pter
137
Gle
ncoe
Alg
ebra
2
Rea
l-W
orl
d P
rob
lem
s w
ith
Ineq
ual
itie
sM
any
real
-wor
ld p
robl
ems
invo
lve
ineq
ual
itie
s.T
he
char
t be
low
sh
ows
som
e co
mm
on p
hra
ses
that
in
dica
te i
neq
ual
itie
s.
�
��
is le
ss t
han
is g
reat
er t
han
is a
t m
ost
is a
t le
ast
is fe
wer
tha
nis
mor
e th
anis
no
mor
e th
anis
no
less
tha
nis
less
tha
n or
equ
al t
ois
gre
ater
tha
n or
equ
al t
o
SPO
RTS
Th
e V
ikin
gs p
lay
36 g
ames
th
is y
ear.
At
mid
seas
on,t
hey
hav
e w
on 1
6 ga
mes
.How
man
y of
th
e re
mai
nin
g ga
mes
mu
st t
hey
win
in
ord
er t
ow
in a
t le
ast
80%
of
all
thei
r ga
mes
th
is s
easo
n?
Let
xbe
th
e n
um
ber
of r
emai
nin
g ga
mes
th
at t
he
Vik
ings
mu
st w
in.T
he
tota
l n
um
ber
ofga
mes
th
ey w
ill
hav
e w
on b
y th
e en
d of
th
e se
ason
is
16 �
x.T
hey
wan
t to
win
at
leas
t 80
%of
th
eir
gam
es.W
rite
an
in
equ
alit
y w
ith
.
16 �
x
0.8(
36)
x
0.8(
36)
�16
x
12.8
Sin
ce t
hey
can
not
win
a f
ract
ion
al p
art
of a
gam
e,th
e V
ikin
gs m
ust
win
at
leas
t 13
of
the
gam
es r
emai
nin
g.
1.PA
RK
ING
FEE
ST
he
city
par
kin
g lo
t ch
arge
s $2
.50
for
the
firs
t h
our
and
$0.2
5 fo
r ea
chad
diti
onal
hou
r.If
th
e m
ost
you
wan
t to
pay
for
par
kin
g is
$6.
50,s
olve
th
e in
equ
alit
y2.
50 �
0.25
(x�
1) �
6.50
to
dete
rmin
e fo
r h
ow m
any
hou
rs y
ou c
an p
ark
you
r ca
r.A
t m
ost
17
ho
urs
PLA
NN
ING
For
Exe
rcis
es 2
an
d 3
,use
th
e fo
llow
ing
info
rmat
ion
.
Eth
an i
s re
adin
g a
482-
page
boo
k fo
r a
book
rep
ort
due
on M
onda
y.H
e h
as a
lrea
dy r
ead
80 p
ages
.He
wan
ts t
o fi
gure
ou
t h
ow m
any
page
s pe
r h
our
he
nee
ds t
o re
ad i
n o
rder
to
fin
ish
th
e bo
ok i
n l
ess
than
6 h
ours
.
2.W
rite
an
in
equ
alit
y to
des
crib
e th
is s
itu
atio
n.
�6
or
6n�
482
�80
3.S
olve
the
ine
qual
ity
and
inte
rpre
t th
e so
luti
on.
Eth
an m
ust
rea
d a
t le
ast
67 p
ages
per
ho
ur
in o
rder
to
fin
ish
th
e b
oo
k in
less
th
an 6
ho
urs
.
BO
WLI
NG
For
Exe
rcis
es 4
an
d 5
,use
th
e fo
llow
ing
info
rmat
ion
.
Fou
r fr
ien
ds p
lan
to
spen
d F
rida
y ev
enin
g at
th
e bo
wli
ng
alle
y.T
hre
e of
th
e fr
ien
ds n
eed
tore
nt
shoe
s fo
r $3
.50
per
pers
on.A
str
ing
(gam
e) o
f bo
wli
ng
cost
s $1
.50
per
pers
on.I
f th
efr
ien
ds p
ool
thei
r $4
0,h
ow m
any
stri
ngs
can
th
ey a
ffor
d to
bow
l?
4.W
rite
an
equ
atio
n t
o de
scri
be t
his
sit
uat
ion
.3(
3.50
) �
4(1.
50)n
�40
5.S
olve
th
e in
equ
alit
y an
d in
terp
ret
the
solu
tion
.T
he
frie
nd
s ca
n b
ow
l at
mo
st
4 st
rin
gs.
482
�80
�� n
Stud
y G
uide
and
Inte
rven
tion
(co
ntin
ued)
Sol
vin
g I
neq
ual
itie
s
Lesson 1-5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
Exer
cise
s
Exam
ple
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A17
Chapter 1 A18 Glencoe Algebra 2
Answers (Lesson 1-5)
Skill
s Pr
acti
ceS
olvi
ng
In
equ
alit
ies
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er o
r in
terv
aln
otat
ion
.Th
en,g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.
2{z
� z�
�8}
2.
3a�
7 �
16{a
� a�
3}
3.16
�3q
�4
{q� q
�4}
4.
20 �
3s�
7s{s
� s
2}
5.3x
�
9{x
� x�
�3}
6.4b
�9
�7
{b� b
�4}
7.2z
��
9 �
5z{z
� z�
3}
8.7f
�9
�3f
�1
{f� f
�2}
9.�
3s�
8 �
5s{s
� s�
�1}
10.7
t�
(t�
4) �
25�t�
t�
�
11.0
.7m
�0.
3m
2m�
4{m
� m�
4}12
.4(5
x�
7) �
13�x
� x�
��o
r
13.1
.7y
�0.
78 �
5{y
� y�
3.4}
14.4
x�
9 �
2x�
1{x
� x�
5}
Def
ine
a va
riab
le a
nd
wri
te a
n i
neq
ual
ity
for
each
pro
ble
m.T
hen
sol
ve.
15.N
inet
een
mor
e th
an a
nu
mbe
r is
les
s th
an 4
2.n
�19
42
;n
23
16.T
he
diff
eren
ce o
f th
ree
tim
es a
nu
mbe
r an
d 16
is
at l
east
8.
3n�
16 �
8;n
�8
17.O
ne h
alf
of a
num
ber
is m
ore
than
6 l
ess
than
the
sam
e nu
mbe
r.n
�n
�6;
n
12
18.F
ive
less
th
an t
he
prod
uct
of
6 an
d a
nu
mbe
r is
no
mor
e th
an t
wic
e th
at s
ame
nu
mbe
r.
6n�
5 �
2n;
n�
5 � 4
1 � 2
�1
01
23
45
67
�1
�2
01
23
45
6
�2
�1
�4
�3
01
23
4�
2�
10
12
34
56
3 � 4
�2
�1
�4
�3
01
23
4�
1�
2�
3�
40
12
34
7 � 2
�1
�2
�3
�4
01
23
4�
1�
20
12
34
56
�2
�1
01
23
45
6�
1�
2�
3�
40
12
34
�2
�1
�4
�3
01
23
4�
10
12
34
56
7
�2
�1
�4
�3
01
23
4�
7�
6�
9�
8�
5�
4�
3�
2�
1
z �
4
Cha
pter
138
Gle
ncoe
Alg
ebra
2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Cha
pter
139
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Sol
ve e
ach
in
equ
alit
y.D
escr
ibe
the
solu
tion
set
usi
ng
set-
bu
ild
er o
r in
terv
aln
otat
ion
.Th
en,g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.8x
�6
10
{x
� x�
2}2.
23 �
4u�
11 {
u� u
�3}
3.�
16 �
8r
0 {r
� r�
�2}
4.
14s
�9s
�5
{s� s
1}
5.9x
�11
�6x
�9 �x
� x�
�6.
�3(
4w�
1) �
18 �w
� w
��
7.1
�8u
�3u
�10
{u
� u�
1}
8.17
.5 �
19 �
2.5x
{x� x
0.
6}
9.9(
2r�
5) �
3 �
7r�
4 {r
� r
4}
10.1
�5(
x�
8) �
2 �
(x�
5) {
x� x
�6}
11.
�
3.5
{x� x
��
1}
12.q
�2(
2 �
q) �
0 �q
� q�
�
13.�
36 �
2(w
�77
) �
�4(
2w�
52)
14.4
n�
5(n
�3)
�3(
n�
1) �
4 {w
� w�
�3}
{n
� n
4}
Def
ine
a va
riab
le a
nd
wri
te a
n i
neq
ual
ity
for
each
pro
ble
m.T
hen
sol
ve.
15.T
wen
ty l
ess
than
a n
um
ber
is m
ore
than
tw
ice
the
sam
e n
um
ber.
n�
20 �
2n;
n
�20
16.F
our
tim
es t
he
sum
of
twic
e a
nu
mbe
r an
d �
3 is
les
s th
an 5
.5 t
imes
th
at s
ame
nu
mbe
r.4[
2n�
(�3)
]
5.5n
;n
4.
8
17.H
OTE
LST
he
Lin
coln
’s h
otel
roo
m c
osts
$90
a n
igh
t.A
n a
ddit
ion
al 1
0% t
ax i
s ad
ded.
Hot
el p
arki
ng
is $
12 p
er d
ay.T
he
Lin
coln
’s e
xpec
t to
spe
nd
$30
in t
ips
duri
ng
thei
r st
ay.
Sol
ve t
he
ineq
ual
ity
90x
�90
(0.1
)x�
12x
�30
�60
0 to
fin
d h
ow m
any
nig
hts
th
eL
inco
ln’s
can
sta
y at
th
e h
otel
wit
hou
t ex
ceed
ing
tota
l h
otel
cos
ts o
f $6
00.
5 n
igh
ts
18.B
AN
KIN
GJa
n’s
acc
oun
t ba
lan
ce i
s $3
800.
Of
this
,$75
0 is
for
ren
t.Ja
n w
ants
to
keep
aba
lan
ce o
f at
lea
st $
500.
Wri
te a
nd
solv
e an
in
equ
alit
y de
scri
bin
g h
ow m
uch
sh
e ca
nw
ith
draw
an
d st
ill
mee
t th
ese
con
diti
ons.
3800
�75
0 �
w�
500;
w�
$255
0
0�
1�
21
23
45
6�
1�
2�
3�
40
12
34
0�
1�
2�
3�
41
23
4�
1�
2�
3�
40
12
34
4 � 34x
�3
2
01
23
45
67
8�
2�
10
12
34
56
�2
�1
�4
�3
01
23
4�
1�
2�
3�
40
12
34
�2
�1
�4
�3
01
23
4�
1�
2�
3�
40
12
34
5 � 42 � 3
�2
�1
�4
�3
01
23
4�
2�
1�
4�
30
12
34
�1
�2
01
23
45
6�
1�
2�
3�
40
12
34
Prac
tice
Sol
vin
g I
neq
ual
itie
s
Lesson 1-5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A18
Chapter 1 A19 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-5)
Cha
pter
140
Gle
ncoe
Alg
ebra
2
1.PA
ND
AS
An
adu
lt p
anda
bea
r w
ill
eat
at l
east
20
pou
nds
of
bam
boo
ever
y da
y.W
rite
an
in
equ
alit
y th
at e
xpre
sses
th
issi
tuat
ion
.b
�20
2.PA
RTY
FA
VO
RS
Jan
elle
wou
ld l
ike
togi
ve a
par
ty b
ag t
o ev
ery
pers
on w
ho
isco
min
g to
her
par
ty.T
he
cost
of
the
part
y ba
g is
$7
per
pers
on.W
rite
an
ineq
ual
ity
that
des
crib
es t
he
nu
mbe
r of
peo
ple
Pth
at s
he
can
in
vite
if
Jan
elle
has
Ddo
llar
s to
spe
nd
on
the
part
y ba
gs.
P�
3.IN
CO
ME
Man
uel t
akes
a jo
b tr
ansl
atin
gE
ngli
sh in
stru
ctio
n m
anua
ls t
o S
pani
sh.
He
wil
l rec
eive
$15
per
pag
e pl
us $
100
per
mon
th.M
anue
l wou
ld li
ke t
o w
ork
for
3 m
onth
s du
ring
the
sum
mer
and
mak
eat
leas
t $1
,500
.Wri
te a
nd s
olve
an
ineq
uali
ty t
o fi
nd t
he m
inim
um n
umbe
rof
pag
es M
anue
l mus
t tr
ansl
ate
in o
rder
to r
each
his
goa
l.15
P�
300
�15
00P
�80
;M
anu
el m
ust
tra
nsl
ate
atle
ast
80 p
ages
.
4.FI
ND
ING
TH
E ER
RO
RT
he
sam
ple
belo
w s
how
s h
ow B
ran
don
sol
ved
5 �
�2x
�7.
Stu
dy h
is s
olu
tion
an
dde
term
ine
if i
t is
cor
rect
.Exp
lain
you
rre
ason
ing.
It is
inco
rrec
t.F
rom
ste
p 2
to
ste
p3,
Bra
nd
on
mu
st c
han
ge
the
dir
ecti
on
of
the
ineq
ual
ity
bec
ause
he
is d
ivid
ing
by
a n
egat
ive
nu
mb
er.
Th
e co
rrec
t an
swer
is x
�
6.
CA
RN
IVA
LSF
or E
xerc
ises
5–7
,use
th
efo
llow
ing
info
rmat
ion
.
On
a F
erri
s w
hee
l at
a c
arn
ival
,on
ly t
wo
peop
le p
er c
ar a
re a
llow
ed.T
he
two
peop
leto
geth
er c
ann
ot w
eigh
mor
e th
an 3
00po
un
ds.L
et x
and
ybe
th
e w
eigh
ts o
f th
epe
ople
.
5.W
rite
an
in
equ
alit
y th
at d
escr
ibes
th
ew
eigh
t li
mit
atio
n i
n t
erm
s of
xan
d y.
x�
y�
300
6.W
rite
an
in
equ
alit
y th
at d
escr
ibes
th
eli
mit
on
th
e av
erag
e w
eigh
t a
of t
he
two
ride
rs.
a�
150
7.R
on a
nd
his
fat
her
wan
t to
go
on t
he
ride
toge
ther
.Ron
’s f
ath
er w
eigh
s 17
5 po
un
ds.
Wh
at i
s th
e m
axim
um
wei
ght
Ron
can
be
for
the
two
to b
e al
low
ed o
n t
he
ride
?12
5 p
ou
nd
s
5<
—2x
— 7
12<
—2x
—6
<x
D 7
Wor
d Pr
oble
m P
ract
ice
Sol
vin
g I
neq
ual
itie
s
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-5
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Cha
pter
141
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Eq
uiv
alen
ce R
elat
ion
sA
rel
atio
n R
on
a s
et A
is a
n e
quiv
alen
ce r
elat
ion
if i
t h
as t
he
foll
owin
g pr
oper
ties
.
Ref
lexi
ve P
rop
erty
For
an
y el
emen
t a
of s
et A
,aR
a.
Sym
met
ric
Pro
per
tyF
or a
ll e
lem
ents
aan
d b
of s
et A
,if
aR
b,t
hen
bR
a.
Tra
nsi
tive
Pro
per
tyF
or a
ll e
lem
ents
a,b
,an
d c
of s
et A
,if
aR
ban
d b
R c
,th
en a
R c
.
Equ
alit
y on
th
e se
t of
all
rea
l n
um
bers
is
refl
exiv
e,sy
mm
etri
c,an
d tr
ansi
tive
.T
her
efor
e,it
is
an e
quiv
alen
ce r
elat
ion
.
In e
ach
of
the
foll
owin
g,a
rela
tion
an
d a
set
are
giv
en.W
rite
yes
if t
he
rela
tion
is
an e
qu
ival
ence
rel
atio
n o
n t
he
give
n s
et.I
f it
is
not
,tel
l w
hic
h o
f th
e p
rop
erti
es i
t fa
ils
to e
xhib
it.
1.�
,{al
l n
um
bers
}n
o;
refl
exiv
e,sy
mm
etri
c
2.
,{al
l tr
ian
gles
in
a p
lan
e}ye
s
3.is
th
e si
ster
of,
{all
wom
en i
n T
enn
esse
e}n
o;
refl
exiv
e
4.
,{al
l n
um
bers
}n
o;
sym
met
ric
5.is
a f
acto
r of
,{al
l n
onze
ro i
nte
gers
}n
o;
sym
met
ric
6.
,{al
l po
lygo
ns
in a
pla
ne}
yes
7.is
th
e sp
ouse
of,
{all
peo
ple
in R
oan
oke,
Vir
gin
ia}
no
;re
flex
ive,
tran
siti
ve
8.⊥
,{al
l li
nes
in
a p
lan
e}n
o;
refl
exiv
e,tr
ansi
tive
9.is
a m
ult
iple
of,
{all
in
tege
rs}
no
;sy
mm
etri
c
10.
is t
he
squ
are
of,{
all
nu
mbe
rs}
no
;re
flex
ive,
sym
met
ric,
tran
siti
ve
11.
��,{a
ll l
ines
in
a p
lan
e}n
o;
refl
exiv
e
12.
has
th
e sa
me
colo
r ey
es a
s,{a
ll m
embe
rs o
f th
e C
leve
lan
d S
ymph
ony
Orc
hes
tra}
yes
13.
is t
he
grea
test
in
tege
r n
ot g
reat
er t
han
,{al
l n
um
bers
}n
o;
refl
exiv
e,sy
mm
etri
c,tr
ansi
tive
14.
is t
he
grea
test
in
tege
r n
ot g
reat
er t
han
,{al
l in
tege
rs}
yes
Enri
chm
ent
Lesson 1-5
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-5
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A19
Chapter 1 A20 Glencoe Algebra 2
Answers (Lesson 1-6)
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Less
on R
eadi
ng G
uide
Sol
vin
g C
omp
oun
d a
nd
Ab
solu
te V
alu
e In
equ
alit
ies
Get
Rea
dy
for
the
Less
on
Rea
d t
he
intr
odu
ctio
n t
o L
esso
n 1
-6 i
n y
our
text
boo
k.
•F
ive
pati
ents
arr
ive
at a
med
ical
lab
orat
ory
at 1
1:30
A.M
.for
a g
luco
se t
oler
ance
tes
t.E
ach
of
them
is
aske
d w
hen
th
ey l
ast
had
som
eth
ing
to e
at o
r dr
ink.
Som
e of
th
e pa
tien
tsar
e gi
ven
th
e te
st a
nd
oth
ers
are
told
th
at t
hey
mu
st c
ome
back
an
oth
er d
ay.E
ach
of
the
pati
ents
is
list
ed b
elow
wit
h t
he
tim
es w
hen
th
ey s
tart
ed t
o fa
st.(
Th
e P.
M.t
imes
ref
er t
oth
e n
igh
t be
fore
.) W
hic
h o
f th
e pa
tien
ts w
ere
acce
pted
for
th
e te
st?
Ora
5:00
A.M
.Ju
anit
a11
:30
P.M
.Ja
son
an
d J
uan
ita
Jaso
n1:
30 A
.M.
Sam
ir5:
00 P
.M.
Rea
d t
he
Less
on
1.a.
Wri
te a
com
pou
nd
ineq
ual
ity
that
say
s,“x
is g
reat
er t
han
�3
and
xis
les
s th
an o
req
ual
to
4.”
�3
x
�4
b.
Gra
ph t
he
ineq
ual
ity
that
you
wro
te i
n p
art
a on
a n
um
ber
lin
e.
2.U
se a
com
pou
nd
ineq
ual
ity
and
set-
buil
der
not
atio
n t
o de
scri
be t
he
foll
owin
g gr
aph
.{x
� x�
�1
or
x�
3}
3.W
rite
a s
tate
men
t eq
uiv
alen
t to
⏐4x
�5⏐
�2
that
doe
s n
ot u
se t
he
abso
lute
val
ue
sym
bol.
4x�
5 �
2 o
r 4x
�5
�
2
4.W
rite
a s
tate
men
t eq
uiv
alen
t to
⏐3x
�7⏐
�8
that
doe
s n
ot u
se t
he
abso
lute
val
ue
sym
bol.
�8
3x
�7
8
Rem
emb
er W
hat
Yo
u L
earn
ed
5.M
any
stu
den
ts h
ave
trou
ble
know
ing
wh
eth
er a
n a
bsol
ute
val
ue
ineq
ual
ity
shou
ld b
etr
ansl
ated
in
to a
n a
nd
or a
n o
rco
mpo
un
d in
equ
alit
y.D
escr
ibe
a w
ay t
o re
mem
ber
wh
ich
of t
hes
e ap
plie
s to
an
abs
olu
te v
alu
e in
equ
alit
y.A
lso
desc
ribe
how
to
reco
gniz
e th
edi
ffer
ence
fro
m a
nu
mbe
r li
ne
grap
h.
Sam
ple
an
swer
:If
th
e ab
solu
te v
alu
eq
uan
tity
is f
ollo
wed
by
a
or
�sy
mb
ol,
the
exp
ress
ion
insi
de
the
abso
lute
val
ue
bar
s m
ust
be
bet
wee
ntw
o n
um
ber
s,so
th
is b
eco
mes
an
and
ineq
ual
ity.
Th
e n
um
ber
lin
e g
rap
h w
ill s
ho
w a
sin
gle
inte
rval
bet
wee
ntw
o n
um
ber
s.If
th
e ab
solu
te v
alu
e q
uan
tity
is f
ollo
wed
by
a �
or
�sy
mb
ol,
it b
eco
mes
an
or
ineq
ual
ity,
and
th
e g
rap
h w
ill s
ho
w t
wo
dis
con
nec
ted
inte
rval
s w
ith
arr
ow
s g
oin
g in
op
po
site
dir
ecti
on
s.
�4
�5
�3
�2
�1
01
23
45
�4
�3
�2
�1
01
23
5�
54
Cha
pter
142
Gle
ncoe
Alg
ebra
2
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-6
Cha
pter
143
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Stud
y G
uide
and
Inte
rven
tion
Sol
vin
g C
omp
oun
d a
nd
Ab
solu
te V
alu
e In
equ
alit
ies
Co
mp
ou
nd
Ineq
ual
itie
sA
com
pou
nd
ineq
ual
ity
con
sist
s of
tw
o in
equ
alit
ies
join
ed b
yth
e w
ord
and
or t
he
wor
d or
.To
solv
e a
com
pou
nd
ineq
ual
ity,
you
mu
st s
olve
eac
h p
art
sepa
rate
ly.
Exa
mpl
e:x
��
4 an
d x
�3
The
gra
ph is
the
inte
rsec
tion
of s
olut
ion
sets
of
two
ineq
ualit
ies.
Exa
mpl
e:x
��
3 or
x�
1T
he g
raph
is t
he u
nion
of
solu
tion
sets
of
two
ineq
ualit
ies.
�5
�4
�3
�2
�1
01
23
45
Or
Co
mp
ou
nd
Ineq
ual
itie
s
�3
�2
�5
�4
�1
01
23
45
An
dC
om
po
un
dIn
equ
alit
ies
Sol
ve �
3 �
2x�
5 �
19.
Gra
ph
th
e so
luti
on s
et o
n a
nu
mb
er l
ine.
�3
�2x
�5
and
2x�
5 �
19�
8 �
2x2x
�14
�4
�x
x�
7
�4
�x
�7
�4
�2
�8
�6
02
46
8
Sol
ve 3
y�
2 �
7 or
2y
�1
��
9.G
rap
h t
he
solu
tion
set
on a
nu
mb
er l
ine.
3y�
2
7or
2y�
1 �
�9
3y
9or
2y�
�8
y
3or
y�
�4
�8
�6
�4
�2
02
46
8
Sol
ve e
ach
in
equ
alit
y.G
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.�
10 �
3x�
2 �
142.
3a�
8 �
23 o
r a
�6
�7
{x� �
4
x�
4}{a
� a
5 o
r a
�52
}
3.18
�4x
�10
�50
4.5k
�2
��
13 o
r 8k
�1
�19
{x� 7
x
15
}{k
� k
�3
or
k�
2.5}
5.10
0 �
5y�
45 �
225
6.b
�2
�10
or
b�
5 �
�4
{y� 2
9 �
y�
54}
{b� b
�
12 o
r b
�18
}
7.22
�6w
�2
�82
8.4d
�1
��
9 or
2d
�5
�11
{w� 4
w
14
}{a
ll re
al n
um
ber
s}
0�
1�
2�
3�
41
23
40
24
68
1012
1416
�24
�12
012
240
1020
3040
5060
7080
3 42 3
�4
�3
�2
�1
01
23
43
57
911
1315
1719
�10
010
2030
4050
6070
�8
�6
�4
�2
02
46
8
1 4
Exam
ple
2
Exer
cise
s
Exam
ple
1
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A20
Chapter 1 A21 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-6)
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Ab
solu
te V
alu
e In
equ
alit
ies
Use
th
e de
fin
itio
n o
f ab
solu
te v
alu
e to
rew
rite
an
abso
lute
val
ue
ineq
ual
ity
as a
com
pou
nd
ineq
ual
ity.
For
all
real
num
bers
aan
d b,
b�
0, t
he fo
llow
ing
stat
emen
ts a
re t
rue.
1.If
⏐a⏐
�b,
the
n �
b�
a�
b.2.
If ⏐a
⏐�
b, t
hen
a�
bor
a�
�b.
The
se s
tate
men
ts a
re a
lso
true
for
�an
d
.
Stud
y G
uide
and
Inte
rven
tion
(c
ontin
ued)
Sol
vin
g C
omp
oun
d a
nd
Ab
solu
te V
alu
e In
equ
alit
ies
Sol
ve �
x�
2�
�4.
Gra
ph
the
solu
tion
set
on
a n
um
ber
lin
e.
By
stat
emen
t 2
abov
e,if
⏐x
�2⏐
�4,
then
x
�2
�4
or x
�2
��
4.S
ubt
ract
ing
2 fr
om b
oth
sid
es o
f ea
ch i
neq
ual
ity
give
s x
�2
or x
��
6.
�8
�6
�4
�2
02
46
8
Sol
ve �
2x
�1
�
5.G
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
By
stat
emen
t 1
abov
e,if
⏐2x
�1⏐
�5,
then
�5
�2x
�1
�5.
Add
ing
1 to
all
th
ree
part
sof
th
e in
equ
alit
y gi
ves
�4
�2x
�6.
Div
idin
g by
2 g
ives
�2
�x
�3.
�4
�2
�8
�6
02
46
8
Sol
ve e
ach
in
equ
alit
y.G
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.⏐3
x�
4⏐�
8�x
� �4
x
�
2.⏐4
s⏐�
1 �
27{s
� s
�6.
5 o
r s
�6.
5}
3.⏐
�3 ⏐�
5{c
� �4
�c
�16
}4.
⏐a�
9⏐
30{a
� a�
�39
or
a�
21}
5.⏐2
f�
11⏐
�9
{f� f
1
or
f�
10}
6.⏐5
w�
2⏐�
28{w
� �6
w
5.
2}
7.⏐1
0 �
2k⏐
�2
{k� 4
k
6}
8.⏐
�5 ⏐�
2 �
10{x
� x
�6
or
x�
26}
9.⏐4
b�
11⏐
�17
�b� �
b
7 �
10.⏐
100
�3m
⏐�
20�m
� m
26o
r m
�40
�2 � 3
3 � 2
�10
010
20�
55
1525
300
24
61
35
78
x 2�8
�4
04
�6
�2
26
8�
40
48
�2
26
1012
�40
�20
020
40�
80
816
�4
412
2024
c 2
�8
�4
04
�6
�2
26
8�
5�
4�
3�
2�
10
12
3
4 � 3
Cha
pter
144
Gle
ncoe
Alg
ebra
2
Exer
cise
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exam
ple
1Ex
ampl
e 2
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Lesson 1-6
Cha
pter
145
Gle
ncoe
Alg
ebra
2
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Skill
s Pr
acti
ceS
olvi
ng
Com
pou
nd
an
d A
bso
lute
Val
ue
Ineq
ual
itie
sW
rite
an
ab
solu
te v
alu
e in
equ
alit
y fo
r ea
ch o
f th
e fo
llow
ing.
Th
en g
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
1.al
l n
um
bers
gre
ater
th
an o
r eq
ual
to
22.
all
nu
mbe
rs l
ess
than
5 a
nd
grea
ter
or l
ess
than
or
equ
al t
o �
2� n
� �
2th
an �
5� n
�
5
3.al
l n
um
bers
les
s th
an �
1 or
gre
ater
4.
all
nu
mbe
rs b
etw
een
�6
and
6� n
�
6th
an 1
� n�
�1
Wri
te a
n a
bso
lute
val
ue
ineq
ual
ity
for
each
gra
ph
.
5.� n
�
16.
� n�
�4
7.� n
� �
38.
� n�
�2.
5
Sol
ve e
ach
in
equ
alit
y.G
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
9.2c
�1
�5
or c
�0
{c� c
�2
10.�
11 �
4y�
3 �
1{y
� �2
�y
�1}
or
c
0}
11.1
0 �
�5x
�5
{x� �
2
x
�1}
12.4
a
�8
or a
��
3{a
� a�
�2
or
a
�3}
13.8
�3x
�2
�23
{x� 2
x
�7}
14.w
�4
�10
or
�2w
�6
all r
eal
nu
mb
ers
15.⏐
t⏐
3{t
� t�
�3
or
t�
3}16
.⏐6x
⏐�
12{x
� �2
x
2}
17.⏐
�7r
⏐�
14{r
� r
�2
or
r�
2}18
.⏐p
�2⏐
��
2�
19.⏐
n�
5⏐�
7{n
� �2
n
12
}20
.⏐h
�1⏐
5
{h� h
��
6 o
r h
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�8
�6
�4
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02
46
8�
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20
24
68
1012
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1�
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41
23
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10
12
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23
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10
12
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41
23
40
12
34
56
78
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01
23
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10
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01
23
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10
12
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01
23
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1�
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30
12
34
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01
23
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30
12
34
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02
46
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10
12
34
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02
46
8�
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3�
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10
12
34
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A21
Chapter 1 A22 Glencoe Algebra 2
Answers (Lesson 1-6)
Cha
pter
146
Gle
ncoe
Alg
ebra
2
Wri
te a
n a
bso
lute
val
ue
ineq
ual
ity
for
each
of
the
foll
owin
g.T
hen
gra
ph
th
eso
luti
on s
et o
n a
nu
mb
er l
ine.
1.al
l n
um
bers
gre
ater
th
an 4
or
less
th
an �
4� n
� �
4
2.al
l n
um
bers
bet
wee
n �
1.5
and
1.5,
incl
udi
ng
�1.
5 an
d 1.
5� n
� �
1.5
Wri
te a
n a
bso
lute
val
ue
ineq
ual
ity
for
each
gra
ph
.
3.� n
� �
104.
� n�
Sol
ve e
ach
in
equ
alit
y.G
rap
h t
he
solu
tion
set
on
a n
um
ber
lin
e.
5.�
8 �
3y�
20 �
52{y
� 4 �
y
24}
6.3(
5x�
2) �
24 o
r 6x
�4
�4
�5x
{x� x
2
or
x�
8}
7.2x
�3
�15
or
3 �
7x�
17{x
� x�
�2}
8.15
�5x
�0
and
5x�
6
�14
{x� x
�3}
9.⏐2
w⏐
5
�w� w
��
or
w�
�10
.⏐y
�5⏐
�2
{x� �
7
x
�3}
11.⏐
x�
8⏐
3{x
� x�
5 o
r x
�11
}12
.⏐2z
�2⏐
�3
�z� �
�z
��
13.⏐
2x�
2⏐�
7 �
�5
{x� �
2 �
x�
0}14
.⏐x⏐
�x
�1
all r
eal n
um
ber
s
15.⏐
3b�
5⏐�
�2
�16
.⏐3n
�2⏐
�2
�1
�n� �
n
�
17.R
AIN
FALL
In 9
0% o
f th
e la
st 3
0 ye
ars,
the
rain
fall
at
Sh
ell
Bea
ch h
as v
arie
d n
o m
ore
than
6.5
in
ches
fro
m i
ts m
ean
val
ue
of 2
4 in
ches
.Wri
te a
nd
solv
e an
abs
olu
te v
alu
ein
equ
alit
y to
des
crib
e th
e ra
infa
ll i
n t
he
oth
er 1
0% o
f th
e la
st 3
0 ye
ars.
� r�
24�
�6.
5;{r
� r
17.5
or
r�
30.5
}
18.M
AN
UFA
CTU
RIN
GA
com
pany
’s g
uide
line
s ca
ll f
or e
ach
can
of s
oup
prod
uced
not
to
vary
from
its
sta
ted
volu
me
of 1
4.5
flu
id o
un
ces
by m
ore
than
0.0
8 ou
nce
s.W
rite
an
d so
lve
anab
solu
te v
alu
e in
equ
alit
y to
des
crib
e ac
cept
able
can
vol
um
es.
� v�
14.5
� �
0.08
;{v
� 14.
42 �
v�
14.5
8}�4
�3
�2
�1
01
23
40
�1
�2
�3
�4
12
34
5 � 31 � 3
0�
1�
2�
3�
41
23
4�
4�
3�
2�
10
12
34
�4
�3
�2
�1
01
23
40
24
68
1012
1416
5 � 21 � 2
�8
�7
�6
�5
�4
�3
�2
�1
0�
4�
3�
2�
10
12
34
5 � 25 � 2
�1
�2
�3
�4
01
23
4�
1�
2�
3�
40
12
34
�2
02
46
810
1214
04
812
1620
2428
32
4 � 3�
4�
3�
2�
10
12
34
�20
�10
010
20
�4
�3
�2
�1
01
23
4
�8
�6
�4
�2
02
46
8
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Prac
tice
S
olvi
ng
Com
pou
nd
an
d A
bso
lute
Val
ue
Ineq
ual
itie
s
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Lesson 1-6
Cha
pter
147
Gle
ncoe
Alg
ebra
2
1.A
QU
AR
IUM
Th
e de
pth
dof
an
aqu
ariu
m t
ank
for
dolp
hin
s sa
tisf
ies
|d�
50|
�5.
Rew
rite
th
is a
s a
com
pou
nd
ineq
ual
ity
that
doe
s n
otin
volv
e th
e ab
solu
te v
alu
e fu
nct
ion
.45
d
< 55
2.H
IKIN
GF
or a
hik
ing
trip
,eve
rybo
dym
ust
bri
ng
at l
east
on
e ba
ckpa
ck.
How
ever
,bec
ause
of
spac
e li
mit
atio
ns,
nob
ody
is a
llow
ed t
o br
ing
mor
e th
antw
o ba
ckpa
cks.
Let
nbe
th
e n
um
ber
ofpe
ople
goi
ng
on t
he
hik
ing
trip
an
d b
beth
e n
um
ber
of b
ackp
acks
all
owed
.Wri
tea
com
pou
nd
ineq
ual
ity
that
des
crib
esh
ow b
and
nar
e re
late
d.n
�b
�2n
3.C
ON
CER
TJa
cin
ta i
s or
gan
izin
g a
larg
efu
nd-
rais
er c
once
rt i
n a
spa
ce w
ith
am
axim
um
cap
acit
y of
10,
000
peop
le.H
ergo
al i
s to
rai
se a
t le
ast
$100
,000
.Tic
kets
cost
$20
per
per
son
.Jac
inta
spe
nds
$50,
000
to p
ut
the
even
t to
geth
er.W
rite
and
solv
e a
com
pou
nd
ineq
ual
ity
that
desc
ribe
s N
,th
e n
um
ber
of a
tten
dees
nee
ded
to a
chie
ve J
acin
ta’s
goa
l.20
N�
50,0
00 �
100,
000
and
N�
10,0
00;T
he
atte
nd
ance
mu
st b
eb
etw
een
7,5
00 a
nd
10,
000
peo
ple
,in
clu
sive
.
4.N
UM
BER
SA
my
is t
hin
kin
g of
tw
on
um
bers
aan
d b.
Th
e su
m o
f th
e tw
on
um
bers
mu
st b
e w
ith
in 1
0 u
nit
s of
zer
o.If
ais
bet
wee
n �
100
and
100,
wri
te a
com
pou
nd
ineq
ual
ity
that
des
crib
es t
he
poss
ible
val
ues
of
b.�
110
b
11
0
AIR
LIN
E B
AG
GA
GE
For
Exe
rcis
es 5
–7,
use
th
e fo
llow
ing
info
rmat
ion
.
An
air
lin
e co
mpa
ny
has
a s
ize
lim
itat
ion
for
carr
y-on
lu
ggag
e.T
he
lim
itat
ion
sta
tes
that
the
sum
of
the
len
gth
,wid
th,a
nd
hei
ght
ofth
e su
itca
se m
ust
not
exc
eed
45 i
nch
es.
5.W
rite
an
in
equ
alit
y th
at d
escr
ibes
th
eai
rlin
e’s
carr
y-on
siz
e li
mit
atio
n.
h�
��
w �
45
6.A
pas
sen
ger
nee
ds t
o br
ing
a so
il s
ampl
eon
th
e pl
ane
that
is
at l
east
1 c
ubi
c fo
ot.
Th
e pa
ssen
ger
is b
rin
gin
g it
in
a s
uit
case
that
is
in t
he
shap
e of
a c
ube
wit
h s
ide
len
gth
sin
ches
.Wri
te a
n i
neq
ual
ity
that
give
s th
e m
inim
um
len
gth
for
s.
s�
12
7.W
rite
a c
ompo
un
d in
equ
alit
y fo
r s
usi
ng
part
s A
an
d B
.Fin
d th
e m
axim
um
an
dm
inim
um
val
ues
for
s.
s�
12 a
nd
3s
�45
;s
is a
t le
ast
12an
d a
t m
ost
15
h
wl
Wor
d Pr
oble
m P
ract
ice
Sol
vin
g C
omp
oun
d a
nd
Ab
solu
te V
alu
e In
equ
alit
ies
Copyright ©Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
AT
E__
____
____
__P
ER
IOD
____
_
1-6
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A22
Chapter 1 A23 Glencoe Algebra 2
An
swer
s
Answers (Lesson 1-6)
Cha
pter
148
Gle
ncoe
Alg
ebra
2
Enri
chm
ent
Con
jun
ctio
ns
and
Dis
jun
ctio
ns
An
abs
olu
te v
alu
e in
equ
alit
y m
ay b
e so
lved
as
a co
mpo
un
d se
nte
nce
.
Sol
ve �2
x�
10.
�2x�
�10
mea
ns
2x�
10 a
nd
2x�
�10
.
Sol
ve e
ach
in
equ
alit
y.x
�5
and
x�
�5.
Eve
ry s
olu
tion
for
�2x�
�10
is
a re
plac
emen
t fo
r x
that
mak
es b
oth
x�
5 an
d x
��
5 tr
ue.
A c
ompo
un
d se
nte
nce
th
at c
ombi
nes
tw
o st
atem
ents
by
the
wor
d an
dis
a
con
jun
ctio
n.
Sol
ve �3
x�
7��
11.
�3x
�7
� 11
mea
ns
3x�
7
11 o
r 3x
�7
��
11.
Sol
ve e
ach
in
equ
alit
y.3x
18
or
3x�
�4
x
6 or
x
��
4 3
Eve
ry s
olu
tion
for
th
e in
equ
alit
y is
a r
epla
cem
ent
for
xth
at m
akes
eit
her
x
6 or
x�
�4 3
tru
e.
A c
ompo
un
d se
nte
nce
th
at c
ombi
nes
tw
o st
atem
ents
by
the
wor
d or
is
a d
isju
nct
ion
.
Sol
ve e
ach
in
equ
alit
y.T
hen
wri
te w
het
her
th
e so
luti
on i
s a
con
jun
ctio
n o
rd
isju
nct
ion
.
1.�4
x��
242.
�x�
7��
8
x�
6 o
r x
�
6;d
isju
nct
ion
x�
15 a
nd
x�
�1;
con
jun
ctio
n
3.�2
x�
5��
14.
�x�
1�
1
x
�2
and
x�
�3;
con
jun
ctio
nx
�2
or
x�
0;d
isju
nct
ion
5.�3
x�
1��
x6.
7 �
�2x�
�5
x�
�1 2�an
d x
��1 4� ;
con
jun
ctio
nx
1
and
x�
�1;
con
jun
ctio
n
7.� 2x
�1
� 7
8.�x
� 34
��
4
x�
12 o
r x
��
16;
dis
jun
ctio
nx
16
an
d x
��
8;co
nju
nct
ion
9.�8
�x�
�2
10.�
5�
2x�
�3
x
6 o
r x
�10
;d
isju
nct
ion
x�
1 an
d x
�4;
con
jun
ctio
n
NA
ME
____
____
____
____
____
____
____
____
____
____
____
__D
ATE
____
____
____
__P
ER
IOD
____
_
1-6
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
Exer
cise
s
Exam
ple
1
Exam
ple
2
A1-A23 A2-01-873971 5/19/06 8:03 AM Page A23