Solving Linear Equations Chapter Questions
1. What are inverse operations? Name them.
2. How do you solve equations?
3. What do you do when an equation has variables on both sides?
4. How do you transform equations? Why would you want to?
Solving Equations Chapter Problems
Inverse Operations
Classwork
1. Name the inverse operation needed to solve for the variable.
a. x + 9 = 17
b. y – 8 = 5
c. m + 5 = 21
d.
𝑤
6
= 12
e. 9v = 108
Homework
2. Name the inverse operation needed to solve for the variable.
a. t – 18 = 54
b. 14x = 228
c. m + 19 = 51
d. 11b = 66
e.
𝑚
4
=2
One Step Equations
NJ Center for Teaching and Learning
~1~
www.njctl.org
Classwork
3. Solve.
a. n + 7 = 20
b. x + 9 = -8
c. a – 15 = 27
d. y – 21 = -15
e. 50 + w = 92
f.
-4 + m = 18
g.
𝑚
= 16
8
h. 30 = 12m
i.
-5m = 25
1
j.
6
𝑡 = 12
k. -10c = -80
n – (-6)= 12
l.
m. -82 + x = -20
−𝑟
n.
2
=5
Homework
4. Solve.
a. n + 9 = 13
b. -14 + b = 21
c. z – 18 = -14
d. -7 + g = -12
e. 19 = 15 + y
f.
g.
b + (-4) = 13
𝑞
3
= 33
h. -18x = -360
i.
x – 11 = 4
NJ Center for Teaching and Learning
~2~
www.njctl.org
j.
1
5
𝑛 = 15
k. -15c = -75
l.
-8 + r = 27
m. 19 + m = 3
n.
–𝑤
8
=1
Two Step Equations
Classwork
Solve.
5. 7x – 2 = 26
6. ½ (m – 3) = 12
7. -6h – 6 = 30
8. 5x + 20 = -20
9. 3 = -3y – 15
10. -24 = 14y – 5
11. 7r – 5 = 10
12. 9 = 16y + 51
13. 13x + 6 = 6
14.
𝑥
−4
+ 11 = 5
Homework
15. 2m – 8 = -28
16.
𝑥
9
−3=8
17. 12m + 20 = -40
−𝑥
18. 3
+ 5 = 21
19. 8r – 27 = -19
NJ Center for Teaching and Learning
~3~
www.njctl.org
6+
20.
𝑘
= 33
3
21. 15 = -4y – 9
22. 8w + 4 = -36
23. 4a – 15 = -23
24. 44 = 5x - 6
Multi-Step Equations
Classwork
Solve.
25. 8s – (8 + 6s) = 20
26. 34 = 2x + 8(x + 3)
27.
28.
3
4
(𝑥 + 9) = 15
2
(𝑚 − 8) = 4
3
29. 35 = 22x – 12x + 5
30. 6(b + 8) = 54
31. 99 = 33x + 3(3x + 5)
32. –t + (5t – 7) = -5
33. 21 – 3(2 – w) = -12
34. 9 = 8b – (2b – 3)
Homework
Solve.
35. 6(m + 4) – 2m = -8
36. 44 = 4(8 + h)
37.
3
4
(8𝑡 − 4) = −2
1
38.
0 = 5 (10ℎ + 15) + ℎ
NJ Center for Teaching and Learning
~4~
www.njctl.org
39. 3(5 – t) – 4t = 18
40. 2(y - 5) = 16
41. 0.1(h + 20) = 3
3𝑧
42. 8
−4=5
43. 8.6 = 6j + 4j
44. 12z – (4z + 6) = 82
More Equations
Classwork
45. 4x = 24
46. -4 = x - 7
47. x + 2 + x = -2
48. 2(3x + 1) = 32
49. 2(-6 + 4x) = -84
50. -6.5x = -29.25
51. -7x - 6/7 = -63 6/7
52. -3x + 9 - 5x = -47
53. 6(-3x -3) = -54
54. 6(7.7x + 4.3) = 339.96
Homework
55. x/ -3 = 6
56. 0 = x - 8
57. 3 + 4x = 31
58. 4 - 6x = -50
59. -29 = x - 7x + 7
60. 3(6x + 7) = 201
61. 7/2 + 3x = 5 9/14
62. -9/4 + 3/2x = 0
63. 5x + 5 - 2x = 5
64. 6.9(1x + 9) = 130.41
NJ Center for Teaching and Learning
~5~
www.njctl.org
Transforming Formulas
Classwork
65. Solve for w. A = lw
66. Solve for m.
𝑣+𝑚
𝑡= 3
67. Solve for b.
16𝑐 − 10𝑏 = 2
68. Solve for h.
𝐴 = 2 𝑏ℎ
69. Solve for 𝜋.
𝑉 = 3 𝜋 𝑟3
1
4
Homework
70. Solve for l. P = 2l + 2w
𝑏+𝑐
71. Solve for c.
𝑝= 5
72. Solve for s.
20𝑥 − 5𝑠 = 8
73. Solve for h.
𝑉 = 2𝜋𝑟 2 ℎ
74. Solve for h.
𝐴 = 2 (𝑏1 + 𝑏2 )ℎ
1
75. The formula for the volume of a right circular cylinder is V = 𝜋 r2h.
The value of h can be expressed as
1)
3)
𝑉 2
𝑟
𝜋
𝑉
𝜋𝑟 2
2)
𝜋𝑟 2
𝑉
4) V- 𝜋𝑟2
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
76. If c = 2m + d, then m is equal to
1)
3)
(𝑐−𝑑)
2
𝑐
𝑑
−2
2)
𝑐
2
−𝑑
4) 𝑑 − 2𝑐
From the New York State Education Department. Office of Assessment Policy, Development and
Administration. Internet. Available from www.nysedregents.org/IntegratedAlgebra; accessed 17, June, 2011.
NJ Center for Teaching and Learning
~6~
www.njctl.org
UNIT REVIEW
Multiple Choice– Choose the correct answer for each question.
1. Name the inverse operation used to solve this equation: x - 12 = 27
a. Multiplication
c. Addition
b. Division
d. Subtraction
2. Name the inverse operation used to solve this equation:
½ m = -28
a. Multiplication
c. Addition
b. Division
d. Subtraction
3. Solve the equation: 1 – 9x = 28
a.
x=3
b.
x = -3
c.
x = 18
d.
x = -18
4. Solve the equation:
3
4
x - 2 = -23
a. p = -21
b. p = 11
c. p = 28
d. p = -28
5. Solve the equation: -2.1k + 13 + 6.5k =24
a. k = 1.26
b. k = - 2.5
c. k = 2.5
d. k = 8.4
NJ Center for Teaching and Learning
~7~
www.njctl.org
6.
Solve the equation: - (2d - 11) = -119
a. d = - 54
b. d = 54
c. d = - 65
d. d = 65
7. Solve the equation: 5(x + 10) = - 425
a. x = 75
b. x = 83
c. x = -95
d. x = -105
Short Constructed Response – Solve each equation and write the correct answer for each question.
8. 4x + 7 = 38
x=
9. 55 = 15t + t - 17
t=
10. 12x –43 - 10x = -83
x=
11. -13(2m - 1) = 65
m=
12. -13 = -4r + 50 + ½ r
r=
13. - 3.1(2w + 5.4) + 4.1w = 42.06
w=
14. -3(-2 - 6v) = -57
v=
NJ Center for Teaching and Learning
~9 ~
www.njctl.org
8
Extended Constructed Response - Solve the problem, showing all work and explaining each step.
15. Cab Ride Company has trip fee of 2.50 and an additional charge of $0.40 for each 1/5 mile. The Yellow Cab Company
has an initial fare of $1.50 and an additional charge of $0.50 for each ¼ m i l e . The S m i t h family is deciding which
of these two cab companies to u s e .
a. Write an equation that represents the cost of each cab company’s fee. Let c = cost
b. For what number of m i l e s will the total cost for each of the cab companies be the same?
c.
The Smith family decides to t a k e a 1 5 m i l e t r i p .
(1) Which cab company should they utilize in order to spend
less money?
(2) How much money will the Smith’s save in their stay in
NY if they have five, fifteen mile trips to take?
16. The Verizon cell phone plan charges a monthly fee of $30 and $0.15/minute. Cingular charges a monthly fee of
$25, and $0.20/minute.
A. Write an equation that represents the cost of each cell phone company’s fee. Let c = cost.
B. For what number of minutes will the total cost for each of the cell phone companies be the same?
C. Mary will talk for approximately 150 minutes/month. What plan should she purchase? Explain your answer.
NJ Center for Teaching and Learning
~9 ~
www.njctl.org
Answer Key
1.
a.
b.
c.
d.
e.
Subtraction
Addition
Subtraction
Multiplication
Division
a.
b.
c.
d.
e.
Addition
Division
Subtraction
Division
Multiplication
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
13
-17
42
6
42
22
128
2.5
-5
72
8
6
62
-10
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
k.
l.
m.
n.
4
35
4
-5
4
17
99
20
15
75
5
35
-16
-8
2.
3.
4.
5. 4
6. 27
7. -6
8. -8
9. -6
10. -19/14
11. 15/7
12. -21/8
13. 0
NJ Center for Teaching and Learning
66. 3t-v
67. (16c-2)/10
68. 2A/b
69. (3V)/(4r3)
70. (P-2w)/2
71. 5p-b
72. (20x-8)/5
73. V/2𝜋r2
74. 2A/(b1+b2)
75. 3
76. 1
14. 24
15. -10
16. 99
17. -5
18. -48
19. 1
20. 81
21. -6
22. -5
23. -2
24. 10
25. 14
26. 1
27. 11
28. 14
29. 3
30. 1
31. 2
32. ½
33. -9
34. 1
35. -8
36. 3
37. 1/6
38. -1
39. -3/7
40. 13
41. 10
42. 24
43. .86
44. 11
45. 6
46. 3
47. -2
48. 5
49. -9
50. 4.5
51. 9
52. 7
53. 2
54. 6.8
55. -18
56. 8
57. 7
58. 9
59. 6
60. 10
61. 5/7
62. 3/2
63. 0
64. 9.9
65. A/l
UNIT REVIEW
1. C
2. A
3. B
4. D
5. C
6. D
7. C
8. 7.75
9. 4.5
10. -20
11. -2
12. 18
13. -28
14. -3.5
15. C = 2.5 + .40(1/5M)
C = 1.50 + .50(1/4M)
B. M = 22.2
C. Yellow cab costs
approximately $3.38/
trip, which is 0.32
cents less than cab
ride company. For five
trips, this is a savings
of $1.60
16. C = 30 + .15M
C = 25 + .20M
B. M = 100 minutes
C. Verizon will cost
approximately
$52.50/month; Cingular
will cost approximately
$55/month. She will save
approximately $2.50 a
month.
~ 10 ~
www.njctl.org