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TRANSCRIPT
©t WKDuBt1aZ 1S0oNfft7wBaHrSeu 1L8LoCx.M K EArl1ln Or5iAgshZtys9 SrOedsLedrRvAeYd4.h D lMpaMdaeQ Nw5iTtuhR JITnxfGignViCtKei IA6l0g1eQbsrNal z1K.E Worksheet by Kuta Software LLC
Algebra 1 Practice by Kareem Gouda www.SKOOLOO.com
Algebra Revision Worksheet with Answers
Solve each equation.
1)
n
+ 7 + 5
n
+ 5 =
7(
5
n
+ 3) −
3(
n
+ 3) 2)
5(
2
m
+ 6) + 8
m
=
−7(
1 −
m
) + 4
3)
−7(
2
r
− 6) =
3(
r
+ 4) − 2
r
4)
8(
x
+ 1) =
7(
3 +
x
)
5)
6(
6
n
− 6) − 4
n
=
−
n
+
6(
1 + 6
n
) 6)
−4
10
v
− 6 = −16
7)
6 − 6
b
− 2 = 64 8)
6
6 − 6
x
= 108
9)
9
n
− 7
3 = 3
10)
4 − 7
a
+ 9 = 27
Solve each inequality and graph its solution.
11)
6
k
3 < 4
−4 −3 −2 −1 0 1 2 3 4 5
12)
−10 +
x
10 ≤ −9
−8 −4 0 4 8 12
13)
x
− 4 − 6 < 0
−3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11
14)
10 +
n
− 7 < 10
−30 −25 −20 −15 −10 −5 0 5 10
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15)
m
+ 5 + 2 < 16
−20 −16 −12 −8 −4 0 4 8
Solve each inequality.
16)
2
x
− 10 <
−2
x
+
2(
4
x
+ 5) 17)
3(
8
p
+ 3) ≥
−4
p
+ 9
18)
7
n
+ 15 ≥
−4 +
6(
n
+ 4) 19)
−40 +
8
b
<
8(
1 − 5
b
)
20)
7 +
7(
1 − 6
r
) >
14 +
6
r
Solve each system by elimination.
21)
−6
x
− 6
y
= −12
−8
x
− 12
y
= 12
22)
−6
x
− 6
y
= 6
4
x
+ 3
y
= −1
23)
−5
x
−
y
= −14
−10
x
− 7
y
= 2
24)
−
x
− 2
y
= −11
6
x
− 10
y
= 22
25)
8
x
− 2
y
= 26
−4
x
− 4
y
= −8
Solve each system by substitution.
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©G lKqu8tsau 9S7ogfEtFwaa2rXeI xLmLDC3.h 2 fA6lLlY hrmiLgphDtLsT irZeTsCemrwvTeJdD.0 N zMfaLdVe3 ew4iOtmhI xIpnbfUiAnkiitheJ 6AWlrgle1bor8a6 51g.i Worksheet by Kuta Software LLC
26)
−
x
+
y
= −3
−7
x
− 7
y
= −7
27)
x
+ 5
y
= −17
3
x
+ 3
y
= −3
28)
−4
x
− 5
y
= −8
x
+ 4
y
= −9
29)
4
x
+
y
= −13
−12
x
− 3
y
= 39
30)
2
x
+
y
= −5
2
x
+ 2
y
= −12
31) The senior classes at High School A and High School B planned separate trips to the water park. The
senior class at High School A rented and filled 2 vans and 4 buses with 142 students. High School B
rented and filled 13 vans and 8 buses with 437 students. Every van had the same number of students in
it as did the buses. Find the number of students in each van and in each bus.
32) A boat traveled 286 miles downstream and back. The trip downstream took 13 hours. The trip back
took 143 hours. What is the speed of the boat in still water? What is the speed of the current?
33) Joe's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 1 senior
citizen ticket and 14 student tickets for a total of $190. The school took in $147 on the second day by
selling 7 senior citizen tickets and 7 student tickets. What is the price each of one senior citizen ticket
and one student ticket?
34) The school that Jessica goes to is selling tickets to a spring musical. On the first day of ticket sales the
school sold 5 adult tickets and 13 child tickets for a total of $265. The school took in $275 on the
second day by selling 10 adult tickets and 9 child tickets. Find the price of an adult ticket and the price
of a child ticket.
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35) Emily and Maria each improved their yards by planting grass sod and ivy. They bought their supplies
from the same store. Emily spent $103 on 7 ft² of grass sod and 4 pots of ivy. Maria spent $138 on 2 ft²
of grass sod and 12 pots of ivy. Find the cost of one ft² of grass sod and the cost of one pot of ivy.
Graph each equation.
36)
y
=
x
− 2 − 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
37)
y
=
x
− 4 − 2
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
38)
y
=
x
− 3 + 2
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
39)
y
=
x
− 2 + 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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40)
y
=
x
− 2 − 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Draw a graph for each inequality.
41) 5 ≥
−
k
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
42) −5 <
−
x
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
43)
b
< 2
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
44)
−
x
< −1
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
45) 5 ≤
m
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
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Sketch the graph of each line.
46)
y
= −4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
47)
6
x
−
y
= 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
48)
6
x
+ 5
y
= −10
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
49)
8
x
+ 5
y
= 15
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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50)
4
x
+ 3
y
= 3
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Sketch the graph of each linear inequality.
51)
y
<
−7
x
+ 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
52)
y
>
−1
4
x
− 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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53)
y
≥
1
3
x
− 3
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
54)
y
<
1
2
x
+ 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
55)
y
≤
3
2
x
− 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Solve each system by graphing.
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56)
4
x
+ 3
y
= −6
2
x
− 3
y
= −12
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
57)
4
x
+
y
= 4
x
+
y
= −2
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
58)
5
x
−
y
= 2
x
−
y
= −2
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
59)
x
−
y
= 2
x
−
y
= −4
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
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60)
2
x
+
y
= −3
2
x
+ 3
y
= 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
Sketch the solution to each system of inequalities.
61)
x
+ 2
y
≥ 4
2
x
+
y
< −1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
62)
x
− 2
y
> 4
2
x
+
y
< 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
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63)
x
+ 2
y
≥ 2
x
− 2
y
≤ −6
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
64)
5
x
+
y
≤ 3
x
−
y
> 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
65)
x
− 3
y
< −9
x
+
y
> −1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
Write an inequality for each graph.
66) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
67) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
68) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
69) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
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70) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
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Algebra 1 Practice by Kareem Gouda www.SKOOLOO.com
Algebra Revision Worksheet with Answers
Solve each equation.
1)
n
+ 7 + 5
n
+ 5 =
7(
5
n
+ 3) −
3(
n
+ 3)
{0}
2)
5(
2
m
+ 6) + 8
m
=
−7(
1 −
m
) + 4
{−3}
3)
−7(
2
r
− 6) =
3(
r
+ 4) − 2
r
{2}
4)
8(
x
+ 1) =
7(
3 +
x
)
{13}
5)
6(
6
n
− 6) − 4
n
=
−
n
+
6(
1 + 6
n
)
{−14}
6)
−4
10
v
− 6 = −16
{1,
1
5}7)
6 − 6
b
− 2 = 64
{−10, 12}
8)
6
6 − 6
x
= 108
{−2, 4}
9)
9
n
− 7
3 = 3
{
16
9,
−2
9}
10)
4 − 7
a
+ 9 = 27
{−2,
22
7 }
Solve each inequality and graph its solution.
11)
6
k
3 < 4
−4 −3 −2 −1 0 1 2 3 4 5
12)
−10 +
x
10 ≤ −9
−8 −4 0 4 8 12
13)
x
− 4 − 6 < 0
−3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11
14)
10 +
n
− 7 < 10
−30 −25 −20 −15 −10 −5 0 5 10
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15)
m
+ 5 + 2 < 16
−20 −16 −12 −8 −4 0 4 8
Solve each inequality.
16)
2
x
− 10 <
−2
x
+
2(
4
x
+ 5)
x
> −5
17)
3(
8
p
+ 3) ≥
−4
p
+ 9
p
≥ 0
18)
7
n
+ 15 ≥
−4 +
6(
n
+ 4)
n
≥ 5
19)
−40 +
8
b
<
8(
1 − 5
b
)
b
< 1
20)
7 +
7(
1 − 6
r
) >
14 +
6
r
r
< 0
Solve each system by elimination.
21)
−6
x
− 6
y
= −12
−8
x
− 12
y
= 12
(9, −7)
22)
−6
x
− 6
y
= 6
4
x
+ 3
y
= −1
(2, −3)
23)
−5
x
−
y
= −14
−10
x
− 7
y
= 2
(4, −6)
24)
−
x
− 2
y
= −11
6
x
− 10
y
= 22
(7, 2)
25)
8
x
− 2
y
= 26
−4
x
− 4
y
= −8
(3, −1)
Solve each system by substitution.
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26)
−
x
+
y
= −3
−7
x
− 7
y
= −7
(2, −1)
27)
x
+ 5
y
= −17
3
x
+ 3
y
= −3
(3, −4)
28)
−4
x
− 5
y
= −8
x
+ 4
y
= −9
(7, −4)
29)
4
x
+
y
= −13
−12
x
− 3
y
= 39
Infinite number of solutions
30)
2
x
+
y
= −5
2
x
+ 2
y
= −12
(1, −7)
31) The senior classes at High School A and High School B planned separate trips to the water park. The
senior class at High School A rented and filled 2 vans and 4 buses with 142 students. High School B
rented and filled 13 vans and 8 buses with 437 students. Every van had the same number of students in
it as did the buses. Find the number of students in each van and in each bus.
Van: 17, Bus: 27
32) A boat traveled 286 miles downstream and back. The trip downstream took 13 hours. The trip back
took 143 hours. What is the speed of the boat in still water? What is the speed of the current?
boat: 12 mph, current: 10 mph
33) Joe's school is selling tickets to a fall musical. On the first day of ticket sales the school sold 1 senior
citizen ticket and 14 student tickets for a total of $190. The school took in $147 on the second day by
selling 7 senior citizen tickets and 7 student tickets. What is the price each of one senior citizen ticket
and one student ticket?
senior citizen ticket: $8, student ticket: $13
34) The school that Jessica goes to is selling tickets to a spring musical. On the first day of ticket sales the
school sold 5 adult tickets and 13 child tickets for a total of $265. The school took in $275 on the
second day by selling 10 adult tickets and 9 child tickets. Find the price of an adult ticket and the price
of a child ticket.
adult ticket: $14, child ticket: $15
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35) Emily and Maria each improved their yards by planting grass sod and ivy. They bought their supplies
from the same store. Emily spent $103 on 7 ft² of grass sod and 4 pots of ivy. Maria spent $138 on 2 ft²
of grass sod and 12 pots of ivy. Find the cost of one ft² of grass sod and the cost of one pot of ivy.
ft² of grass sod: $9, pot of ivy: $10
Graph each equation.
36)
y
=
x
− 2 − 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
37)
y
=
x
− 4 − 2
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
38)
y
=
x
− 3 + 2
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
39)
y
=
x
− 2 + 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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40)
y
=
x
− 2 − 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Draw a graph for each inequality.
41) 5 ≥
−
k
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
42) −5 <
−
x
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
43)
b
< 2
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
44)
−
x
< −1
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
45) 5 ≤
m
−7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
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Sketch the graph of each line.
46)
y
= −4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
47)
6
x
−
y
= 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
48)
6
x
+ 5
y
= −10
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
49)
8
x
+ 5
y
= 15
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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50)
4
x
+ 3
y
= 3
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Sketch the graph of each linear inequality.
51)
y
<
−7
x
+ 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
52)
y
>
−1
4
x
− 4
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
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53)
y
≥
1
3
x
− 3
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
54)
y
<
1
2
x
+ 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
55)
y
≤
3
2
x
− 1
−6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6
−6
−5
−4
−3
−2
1
2
3
4
5
6
Solve each system by graphing.
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56)
4
x
+ 3
y
= −6
2
x
− 3
y
= −12
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
(−3, 2)
57)
4
x
+
y
= 4
x
+
y
= −2
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
(2, −4)
58)
5
x
−
y
= 2
x
−
y
= −2
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
(1, 3)
59)
x
−
y
= 2
x
−
y
= −4
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
No solution
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60)
2
x
+
y
= −3
2
x
+ 3
y
= 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
(−3, 3)
Sketch the solution to each system of inequalities.
61)
x
+ 2
y
≥ 4
2
x
+
y
< −1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
62)
x
− 2
y
> 4
2
x
+
y
< 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
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63)
x
+ 2
y
≥ 2
x
− 2
y
≤ −6
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
64)
5
x
+
y
≤ 3
x
−
y
> 3
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
65)
x
− 3
y
< −9
x
+
y
> −1
−5 −4 −3 −2 −1 0 1 2 3 4 5
−5
−4
−3
−2
−1
1
2
3
4
5
Write an inequality for each graph.
66) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
x
≤ −4
67) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
x
> −1
68) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
a
> 2
69) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
a
≥ 6
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70) −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7
p
≥ −4
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