Solving Linear Equations Chapter Questionswsrmsteamkeystone.weebly.com/uploads/1/3/4/8/... · Solving Equations Chapter Problems Inverse Operations Classwork 1. Name the inverse operation

NJ Center for Teaching and Learning ~ 1 ~ www.njctl.org

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. �

�= 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


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


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


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


l. -8 + r = 27

m. 19 + m = 3

n. –�

�= 1


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


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


20. -24 = 14y – 5

21. 7r – 5 = 10

22. 9 = 16y + 51

23. 13x + 6 = 6

24. �

��+ 11 = 5


Homework

25. 2m – 8 = -28

26. �

�− 3 = 8

27. 12m + 20 = -40

28.

��

�+ 5 = 21


29. 8r – 27 = -19

30. 6 +

�3

= 33

31. 15 = -4y – 9

32. 8w + 4 = -36

33. 4a – 15 = -23


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


Multi-Step Equations

Classwork

Solve.

45. 8s – (8 + 6s) = 20

46. 34 = 2x + 8(x + 3)

47. �

�� + 9� = 15

48.

23

�! − 8� = 4


49. 35 = 22x – 12x + 5

50. 6(b + 8) = 54

51. 99 = 33x + 3(3x + 5)

52. –t + (5t – 7) = -5


53. 21 – 3(2 – w) = -12

54. 9 = 8b – (2b – 3)

Homework

Solve.

55. 6(m + 4) – 2m = -8

56. 44 = 4(8 + h)


57. �

��8� − 4� = −2

58. 0 =

1

5�10ℎ + 15� + ℎ

59. 3(5 – t) – 4t = 18

60. 2(y - 5) = 16


61. 0.1(h + 20) = 3

62.

�%

�− 4 = 5

63. 8.6 = 6j + 4j

64. 12z – (4z + 6) = 82


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.


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.


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


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


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


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


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


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


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.


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.

NJ Center for Teaching and Learning ~28 ~ www.njctl.org

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


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.


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?


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?


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.


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


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.

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Solving Linear Equations Chapter Questionswsrmsteamkeystone.weebly.com/uploads/1/3/4/8/... · Solving Equations Chapter Problems Inverse Operations Classwork 1. Name the inverse operation