geometry section 0-5 1112
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Section 0-5Linear Equations
Wednesday, September 14, 2011
Essential Question
• How do you use Algebra to solve linear equations?
Wednesday, September 14, 2011
Things to Remember
Wednesday, September 14, 2011
Things to Remember
• Isolate the variable
Wednesday, September 14, 2011
Things to Remember
• Isolate the variable
• Do the opposite operations
Wednesday, September 14, 2011
Things to Remember
• Isolate the variable
• Do the opposite operations
• Check your answers
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8 2
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8 2 2
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8 2 2
b = 4
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8
Check:
2 2
b = 4
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8
Check:
2(4)+12 = 20
2 2
b = 4
Wednesday, September 14, 2011
Example 1
a. x −18 = −4
Solve.
b. 2b +12 = 20 +18 +18
x =14
Check:
14 −18 = −4
−12 −12 2b = 8
Check:
2(4)+12 = 20
2 2
b = 4
8 +12 = 20Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5 5 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25 5 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5(25) =125
5 5
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5(25) =125
5 5
(−6)(−
r
6) = 5(−6)
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5(25) =125 r = −30
5 5
(−6)(−
r
6) = 5(−6)
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5(25) =125 Check: r = −30
5 5
(−6)(−
r
6) = 5(−6)
Wednesday, September 14, 2011
Example 1
c. 5t =125
Solve.
d. −
r
6= 5
t = 25
Check:
5(25) =125 Check: r = −30
5 5
(−6)(−
r
6) = 5(−6)
−−306
= 5
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8
32
⎛⎝⎜
⎞⎠⎟
23
h⎛⎝⎜
⎞⎠⎟= 8
32
⎛⎝⎜
⎞⎠⎟
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8
32
⎛⎝⎜
⎞⎠⎟
23
h⎛⎝⎜
⎞⎠⎟= 8
32
⎛⎝⎜
⎞⎠⎟
h =12
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8 Check:
32
⎛⎝⎜
⎞⎠⎟
23
h⎛⎝⎜
⎞⎠⎟= 8
32
⎛⎝⎜
⎞⎠⎟
h =12
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8 Check:
23
(12)+ 9 =17
32
⎛⎝⎜
⎞⎠⎟
23
h⎛⎝⎜
⎞⎠⎟= 8
32
⎛⎝⎜
⎞⎠⎟
h =12
Wednesday, September 14, 2011
Example 1
e.
23
h + 9 =17
Solve.
−9 −9
23
h = 8 Check:
23
(12)+ 9 =17
32
⎛⎝⎜
⎞⎠⎟
23
h⎛⎝⎜
⎞⎠⎟= 8
32
⎛⎝⎜
⎞⎠⎟
h =12
8 + 9 =17
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−4m −4m
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−4m −4m −12 −12
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3m −4m −4m −12 −12
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3m −4m −4m −12 −12
3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3m −4m −4m −12 −12
3 3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3m
−5 = m
−4m −4m −12 −12
3 3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3mCheck:
−5 = m
−4m −4m −12 −12
3 3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3mCheck:
4(−5)− 3 = 7(−5)+12
−5 = m
−4m −4m −12 −12
3 3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3mCheck:
4(−5)− 3 = 7(−5)+12
−5 = m −20 − 3 = −35 +12
−4m −4m −12 −12
3 3
Wednesday, September 14, 2011
Example 1
f. 4m − 3 = 7m +12
Solve.
−15 = 3mCheck:
4(−5)− 3 = 7(−5)+12
−5 = m −20 − 3 = −35 +12
−4m −4m −12 −12
3 3
−23 = −23
Wednesday, September 14, 2011
Problem Set
Wednesday, September 14, 2011
Problem Set
p. P12 #1-36, multiples of 3
“When you make a mistake, there are only three things you should ever do about it: admit it, learns from it, and don’t
repeat it.” - Paul “Bear” BryantWednesday, September 14, 2011
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