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.
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.
NJ Center for Teaching and Learning
www.njctl.org
One Step Equations
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.
h. 30 = 12m
i.
-5m = 25
j.
k. -10c = -80
l.
n – (-6)= 12
m. -82 + x = -20
n.
NJ Center for Teaching and Learning
www.njctl.org
Homework
4. Solve.
a. n + 9 = 13
b. -14 + b = 21
c. z – 18 = -14
d. -7 + g = -12
e. 19 = 15 + y
f.
b + (-4) = 13
g.
h. -18x = -360
i.
x – 11 = 4
j.
k. -15c = -75
l.
-8 + r = 27
m. 19 + m = 3
n.
NJ Center for Teaching and Learning
www.njctl.org
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.
Homework
15. 2m – 8 = -28
16.
17. 12m + 20 = -40
18.
19. 8r – 27 = -19
20.
21. 15 = -4y – 9
22. 8w + 4 = -36
23. 4a – 15 = -23
24. 44 = 5x - 6
NJ Center for Teaching and Learning
www.njctl.org
Multi-Step Equations
Classwork
Solve.
25. 8s – (8 + 6s) = 20
26. 34 = 2x + 8(x + 3)
27.
28.
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)
NJ Center for Teaching and Learning
www.njctl.org
Homework
Solve.
35. 6(m + 4) – 2m = -8
36. 44 = 4(8 + h)
37.
38.
39. 3(5 – t) – 4t = 18
40. 2(y - 5) = 16
41. 0.1(h + 20) = 3
42.
43. 8.6 = 6j + 4j
44. 12z – (4z + 6) = 82
NJ Center for Teaching and Learning
www.njctl.org
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
NJ Center for Teaching and Learning
www.njctl.org
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
www.njctl.org
Transforming Formulas
Classwork
65. Solve for w. A = lw
66. Solve for m.
67. Solve for b.
68. Solve for h.
69. Solve for
.
Homework
70. Solve for l. P = 2l + 2w
71. Solve for c.
72. Solve for s.
73. Solve for h.
74. Solve for h.
75. The formula for the volume of a right circular cylinder is V = πr2h.
The value of h can be expressed as
πr 2
V 2
r
(1)
(3)
V
π
(2)
V
πr 2
(4) V – πr2
76. If c = 2m + d, then m is equal to
c−
d
(1)
(3) c −
2
d
2
(4) d − 2c
(2) c −
d
2
NJ Center for Teaching and Learning
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:
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
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
www.njctl.org
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
www.njctl.org