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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?
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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. �
�= 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. �
�= 2
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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. �
�= 16
h. 30 = 12m
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i. -5m = 25
j.
�� = 12
k. -10c = -80
l. n – (-6)= 12
m. -82 + x = -20
n. �
�= 5
Homework
4. Solve.
a. n + 9 = 13
b. -14 + b = 21
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c. z – 18 = -14
d. -7 + g = -12
e. 19 = 15 + y
f. b + (-4) = 13
g. �
�= 33
h. -18x = -360
i. x – 11 = 4
j.
�� = 15
k. -15c = -75
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l. -8 + r = 27
m. 19 + m = 3
n. –�
�= 1
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Translating and Solving One Step Equations
Classwork
Translate and solve
5. Three more than x is nine
6. The quotient of x and 12 is -2
7. Twice a number is -6
8. Seven less than a number is 84
9. Eight increased by x is 49
Homework
Translate and solve
10. Fourteen is six less than a number
11. Three is the same as a number divided by -5
12. The quotient of x and -5 is 10
13. The product of -9 and a number is -81
14. A number subtracted by 37 is 62
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Two Step Equations
Classwork
Solve.
15. 7x – 2 = 26
16. ½ (m – 3) = 12
17. -6h – 6 = 30
18. 5x + 20 = -20
19. 3 = -3y – 15
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20. -24 = 14y – 5
21. 7r – 5 = 10
22. 9 = 16y + 51
23. 13x + 6 = 6
24. �
��+ 11 = 5
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Homework
25. 2m – 8 = -28
26. �
�− 3 = 8
27. 12m + 20 = -40
28.
��
�+ 5 = 21
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29. 8r – 27 = -19
30. 6 +
�3
= 33
31. 15 = -4y – 9
32. 8w + 4 = -36
33. 4a – 15 = -23
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34. 44 = 5x – 6
Translating and Solving Two Step Equations
Classwork
Translate and solve.
35. Eight more than two times a number is 56
36. The quotient of a number and four minus 16 is 40
37. 6 times the sum of n and 11 is 30
38. 32 minus twice p is 31
39. Three times a number plus three is forty two
Homework
Translate and solve.
40. The product of a number and 24, plus three is the same as -21
41. The sum of eighteen and twice a number is equal to ninety
42. Twenty seven less than three times a number is 6
43. Five times number divided into 4 equal parts is the same as 25
44. Three more than the product of a number and six is twenty one
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Multi-Step Equations
Classwork
Solve.
45. 8s – (8 + 6s) = 20
46. 34 = 2x + 8(x + 3)
47. �
��� + 9� = 15
48.
23
�! − 8� = 4
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49. 35 = 22x – 12x + 5
50. 6(b + 8) = 54
51. 99 = 33x + 3(3x + 5)
52. –t + (5t – 7) = -5
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53. 21 – 3(2 – w) = -12
54. 9 = 8b – (2b – 3)
Homework
Solve.
55. 6(m + 4) – 2m = -8
56. 44 = 4(8 + h)
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57. �
��8� − 4� = −2
58. 0 =
1
5�10ℎ + 15� + ℎ
59. 3(5 – t) – 4t = 18
60. 2(y - 5) = 16
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61. 0.1(h + 20) = 3
62.
�%
�− 4 = 5
63. 8.6 = 6j + 4j
64. 12z – (4z + 6) = 82
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Consecutive Integer Problems
Classwork
Translate and solve
65. Find two consecutive integers that have a sum of -17.
66. Find two consecutive integers that have a sum of 241.
67. Find three consecutive integers that have a sum of 0.
68. Find three consecutive integers that have a sum of 15.
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69. Find three consecutive even integers that have a sum -12.
70. Find three consecutive odd integers that have a sum of 39.
Homework
Translate and solve
71. Find two consecutive integers that have a sum of -87.
72. Find two consecutive integers that have a sum of 1143.
73. Find three consecutive integers that have a sum of 633
74. Find three consecutive integers that have a sum of -2265.
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75. Find three consecutive even integers that have a sum 90.
76. Find three consecutive odd integers that have a sum of 159.
More Equations
Classwork
77. 4x = 24
78. -4 = x - 7
79. x + 2 + x = -2
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80. 2(3x + 1) = 32
81. 2(-6 + 4x) = -84
82. -6.5x = -29.25
83. -7x - 6/7 = -63 6/7
84. -3x + 9 - 5x = -47
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85. 6(-3x -3) = -54
86. 6(7.7x + 4.3) = 339.96
Homework
87. x/ -3 = 6
88. 0 = x - 8
89. 3 + 4x = 31
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90. 4 - 6x = -50
91. -29 = x - 7x + 7
92. 3(6x + 7) = 201
93. 7/2 + 3x = 5 9/14
94. -9/4 + 3/2x = 0
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95. 5x + 5 - 2x = 5
96. 6.9(1x + 9) = 130.41
Transforming Formulas
Classwork
97. Solve for w. A = lw
98. Solve for m. � =&+!
3
99. Solve for b. 16' − 10( = 2
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100. Solve for h. ) =1
2(ℎ
101. Solve for *. + =4
3*,3
Homework
102. Solve for l. P = 2l + 2w
103. Solve for c. - =(+'
5
104. Solve for s. 20� − 5. = 8
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105. Solve for h. + = 2*,�ℎ
106. Solve for h. ) =1
2�( + (��ℎ
107. The formula for the volume of a right circular cylinder is V = *r2h.
The value of h can be expressed as
1) /
0,2 2)
0 1
/
3) /
0 1 4) V-*,2
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.
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108. If c = 2m + d, then m is equal to
1) �2�3�
� 2)
2
�− 4
3) 2
3− 2 4) 4 − 2'
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.
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UNIT REVIEW
Multiple Choice– Choose the correct answer for each question.
1. Translate the following three more than the product of six and a number x.
a. 6 + 3x
b. 6x + 3
c. 3x + 6
d. 3 + 6x
2. Translate the following;
The product of the sum of twelve and a number x and the difference a number x and two
a. (12+x) (x-2)
b. (12x)(2x)
c. 12x -2x
d. (12-x)(x+2)
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
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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
6. Solve the equation: - (2d - 11) = -119
a. d = - 54
b. d = 54
c. d = - 65
d. d = 65
Short Constructed Response – Solve each equation and write the correct answer for each question.
7. Solve the equation: 5(x + 10) = - 425 Write the answer in the box
8. 4x + 7 = 38 Write the answer in the box.
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9. 55 = 15t + t - 17 Write the answer in the box.
10. 12x –43 - 10x = -83 Write the answer in the box.
11. -13(2m - 1) = 65 Write the answer in the box.
12. -13 = -4r + 50 + ½ r Write the answer in the box.
13. Translate and solve. The sum of two consecutive integers is 47. What are the two integers?
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Extended Constructed Response - Solve the problem, showing all work and explaining each step.
14. 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 Sm i t h family is deciding which of these two cab companies to use .
a. Write an equation that represents the cost of each cab company’s fee. Let c = cost
b. For what number of m i les will the total cost for each of the cab companies be the same?
c. The Smith family decides to t ake a 15 m i l e t r i p .
(1) Which cab company should they ut i l ize 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?
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15. 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.
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Answer Key
1.
a. Subtraction
b. Addition
c. Subtraction
d. Multiplication
e. Division
2.
a. Addition
b. Division
c. Subtraction
d. Division
e. Multiplication
3.
a. 13
b. -17
c. 42
d. 6
e. 42
f. 22
g. 128
h. 2.5
i. -5
j. 72
k. 8
l. 6
m. 62 n. -10
4.
a. 4
b. 35
c. 4
d. -5
e. 4
f. 17
g. 99
h. 20
i. 15
j. 75
k. 5
l. 35
m. -16 n. -8
5. x+3 = 9 x=6
6. x/12 = -2 x = -24
7. 2x = -6 x = -3
8. n – 7 = 84 n = 91
9. 8 + x = 49 x = 41
10. 14 = x – 6 x = 20 11. 3 = n / -5 n = -15 12. x / -5 = 10 x = -50 13. -9x = -81 x = 9 14. n – 37 = 62 n = 99 15. 4
16. 27 17. -6 18. -8 19. -6 20. -19/14 21. 15/7 22. -21/8 23. 0 24. 24 25. -10 26. 99 27. -5 28. -48 29. 1 30. 81 31. -6 32. -5 33. -2 34. 10 35. 2x + 8 = 56 x = 24 36. x / 4 – 16 = 40 x = 224 37. 6( n+1 ) = 30 n = -6 38. 32 – 2p = 30 p = 1 39. 3n + 3 = 42 n = 13 40. 24n + 3 = -21 n = -1 41. 18 + 2n = 90 n = 36 42. 3n – 27 = 6 n = 11 43. 5n / 4 = 25 n= 20 44. 6n + 3 = 21 n = 3 45. 14 46. 1 47. 11 48. 14 49. 3 50. 1 51. 2 52. ½ 53. -9 54. 1 55. -8 56. 3 57. 1/6 58. -1 59. -3/7 60. 13 61. 10 62. 24 63. .86 64. 11 65. -8, -9 66. 121, 120 67. -1, 0, 1 68. 4, 5, 6 69. -2, -4, -6
70. 11, 13, 15 71. -43, -44 72. 571, 572 73. 210, 211, 212 74. -754, -755, -756 75. 28, 30, 32 76. 51, 53, 55 77. 6 78. 3 79. -2 80. 5 81. -9 82. 4.5 83. 9 84. 7 85. 2 86. 6.8 87. -18 88. 8 89. 7 90. 9 91. 6 92. 10 93. 5/7 94. 3/2 95. 0 96. 9.9 97. A/l 98. 3t-v 99. (16c-2)/10 100. 2A/b
101. (3V)/(4r3)
102. (P-2w)/2
103. 5p-b
104. (20x-8)/5
105. V/2*r2
106. 2A/(b1+b2)
107. 3
108. 1
UNIT REVIEW
1. B
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
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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.