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Equations & Inequalities Chapter Questions

1. What are inverse operations? Name them.

2. How do you solve equations?

3. What are two different ways to solve equations with fractional distributive property?

4. What do you do when an equation has variables on both sides?

5. How do we translate a statement into an inequality?

6. Explain the steps to graphing an inequality on a number line.

7. How is solving an inequality much like solving a linear equation?


Equations Chapter Problems

Solving an Equation for a Variable

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. 126

w

e. 9v = 108

2) Whose method of solving the equation is better? Explain your answer.

Michael Amanda

𝑥 + 18 = 29 𝑥 + 18 = 29

−18 − 18 −29 − 29

𝑥 = 11 𝑥 − 11 = 0

+11 + 11

𝑥 = 11

Homework

3) 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. 24

m

4) Whose method of solving the equation is better? Explain your answer.

Jack Lisa

12𝑥 = 120 12𝑥 = 120

120 120 12 12

(10)𝑥

10= 1(10) 𝑥 = 10

𝑥 = 10


One Step Equations

Classwork

5) 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. 168

m

h. 30 = 12m

i. -5m = 25

j. 126

1t

k. -10c = -80

l. n – (-6)= 12

m. -82 + x = -20

n. 52

r

o. r – 3.4 = 7.1

p. 𝑔

2.5= 1.8

q. 4.8m = 43.2

r. 3

4𝑡 =

9

20

s. 32

3+ 𝑚 = 5

1

6

Homework

6) 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. 333

q

h. -18x = -360

i. x – 11 = 4

j. 155

1n

k. -15c = -75

l. -8 + r = 27

m. 19 + m = 3


n. 18

w

o. p – 4.8 = 11.2

p. 𝑔

3.4= 2.2

q. 3.6m = 25.2

r. 2

5𝑡 =

8

25

s. 55

6+ 𝑚 = 3

5

12

Two Step Equations

Classwork

Solve. 0.5(m – 3) = 12

7) 7x – 2 = 26

8) 2m – 6 = 48

9) -6h – 6 = 30

10) 5x + 20 = -20

11) 3 = -3y – 15

12) -24 = 14y – 5

13) 7r – 5 = 10

14) 9 = 16y + 51

15) 13x + 6 = 6

16)

5114

x

17) -4.5x + 12.3 = -23.7

18) 𝑥

5+ 4 = 4.3

19) −𝑥

3+ (−7.2) = −2.1

20) 5.4x – 8.3 = 14.38

21) 𝑥

3− 14 = −8

Homework

22) 2m – 8 = -28

23)

839

x

24) 12m + 20 = -40

25)

2153

x

26) 8r – 27 = -19


27)

333

6 k

28) 15 = -4y – 9

29) 8w + 4 = -36

30) 4a – 15 = -23

31) 44 = 5x – 6

32) -3.7x + 5.6 = -5.87

33) 𝑥

5+ 3.5 = 4.16

34) −𝑥

4+ (−9.8) = −5.6

35) 3.7x – 2.2 = 16.3

36) 𝑥

6− 3.7 = 11

Multi-Step Equations

Classwork

Solve.

37) 8s – (8 + 6s) = 20

38) 34 = 2x + 8(x + 3)

39) 3(𝑥 + 9) = 60

40) 2(𝑚 − 8) = 12

41) 35 = 22x – 12x + 5

42) 6(b + 8) = 54

43) 99 = 33x + 3(3x + 5)

44) –t + (5t – 7) = -5

45) 21 – 3(2 – w) = -12

46) 9 = 8b – (2b – 3)

47) 4.5r – 2r + 3(r – 1) = 10.75

48) 1.2(x – 8) + 2.4(x + 1) =7.2

49) 4.9m + (-3.2m) – 13 = -2.63

50) 4(2.25w + 3.1) – 2.75w = 44.9

Homework

Solve.


51) 6(m + 4) – 2m = -8

52) 44 = 4(8 + h)

53) 0.75(8𝑡 − 4) = −2

54) 3(5 – t) – 4t = 18

55) 2(y - 5) = 16

56) 0.1(h + 20) = 3

57) 7y + 3(8 – y) = -12

58) 8.6 = 6j + 4j

59) 12z – (4z + 6) = 82

60) 5.4d – 2.3d + 3(d – 4) = 16.67

61) 2.6f – 1.3(3f – 4) = 6.5

62) -5.3m + (-3.9m) – 17 = -94.28

63) 6(3.5y + 4.2) – 2.75y = 134.7

Distributing Fractions in Equations

Classwork

64) 3

4(𝑥 + 9) = 15

65) 2

3(𝑚 − 8) = 4

66) 1

8(𝑏 + 2) =

3

8

67) 1

7(1x - 4) = -

1

2

68) 2

5 ( - 3 - 2x) =

18

5

69) 4

5(𝑗 + 5) =

2

5

70) 3

4(8𝑥 + 12) = 21

71) 1

2(8𝑟 + 10) = 17

72) 5𝑥

8+ 9 = 4

73) 5

9𝑥 −

4

3=

7

9

74) 10)83

2(3

3

22 pp

75) −51

4𝑢 + 2 (

3

8𝑢 − 9) =

5

2

Homework

76) 2

9(𝑥 + 4) = 6


77) 5

8(3𝑥 + 7) = 10

78) 3

10(𝑥 − 3) =

6

10

79) 2

3(𝑚 + 2) =

4

5

80) 3

4(2𝑥 + 7) =

9

4

81) 6

7(2𝑥 − 12) =

12

7

82) 2

3(6𝑥 + 18) = 20

83) 6

5(10𝑧 + 15) = −6

84) 548

3

z

85) 1

2𝑥 +

3

4= −

7

8

86) 25.79)124

3(4

4

13 pp

87) 31

2𝑤 − 2 (

5

6𝑤 + 2) = −

1

3

Writing and Solving Algebraic Equations

Classwork

PARCC-type Questions:

88) Write an equation then solve.

a. You sold 4 more than three times as many newspapers this week as last week. If you sold

112 altogether, how many did you sell this week?

b. Find the width of a rectangle if its length is 5 more than the width and its perimeter is 90 cm.

c. Four times the sum of a number and -3 is 27 less than the number.

d. Three times twenty-one more than a number is twelve. What is the number?

89) Selina, Elena, and Peter all worked on the same homework assignment. At 6:00 pm Selina had

finished 27

50 of the work, Elena had finished 2/3 of the work, and Peter finished 0.63 of his

homework. Who finished the least amount of homework by 6:00pm.

90) Rafael has 3 times as many blue marbles as he does red marbles. He has a total of 124 marbles.

How many red marbles does he have? How many blue marbles does he have?

91) Luna is going bowling. Shoe rental cost $3 and the lane cost $2 per game. If Luna paid a total of

$17, how many games did she bowl?

92) Audra and Tina are shopping at the Tanger Outlets in Rehoboth Beach, DE. There is no

additional sales tax in the state of Delaware.

Part A

At the GUESS Factory Store, Audra purchased 2 pairs of jeans that cost $42 each and 4 shirts.

The cost of Audra’s total purchase was $132. Write an equation that can be used to find n, the

number of shirts that Audra purchased. Drag and drop the appropriate variable or number into

each box.

132 6 2 90 84 n 42 4

∙ + =


Part B

At the Banana Republic Store, Tina buys 3 T-shirts and 2 skirts. Each T-shirt costs $22.50. Tina

pays the clerk $200 and gets $24.50 in change. What is the cost, in dollars, of one skirt?

Homework

PARCC-type Questions:

93) Write an equation then solve.

a. You sell brownies for $3 each. You sold 12 more this week than last. Altogether, you made

$84. How many brownies did you sell each week?

b. Find the length of a rectangle if its width is 13 less than the length and its perimeter is 90 cm.

c. Six times the difference of a number and 9 is 19 less than the number.

d. Eight times seven more than a number is sixteen. What is the number?

94) Lucas, Jerrell, and Brianna all ran a marathon. Lucas ran 5/9 of the marathon, Jerrell ran 7

11 of the

marathon, and Brianna ran 0.46 of the marathon. Who is in the lead?

95) Lorena had 2 times as many pencils as her brother. In total they have 27 pencils. How many

pencils does Lorena have? How many does her brother have?

96) Jose went to an all-you-can-eat buffet. He paid $15 for his meal and $2 for each soda. If Jose

spent $21, how many sodas did he buy?

97) Audra and Tina are shopping at the Tanger Outlets in Rehoboth Beach, DE. There is no

additional sales tax in the state of Delaware.

Part A

At the Aeropostale Store, Audra purchased 3 wallets that cost $12 each and 2 tote bags. The

cost of Audra’s total purchase was $76. Write an equation that can be used to find n, the number

of tote bags that Audra purchased. Drag and drop the appropriate variable or number into each

box.

Part B

At the same store (Aeropostale), Tina buys 2 pairs of sunglasses and 5 scarves. Each scarf

costs $11. Tina pays the clerk $80 and gets $11 in change. What is the cost, in dollars, of one

pair of sunglasses?

2 12 24 76 36 n 3 1.5

∙ + =


Graphing & Writing Inequalities with One Variable

Classwork

98) Write an inequality for each sentence below, and then graph the solutions of each inequality on a

number line.

a. y is less than 8.

b. f is greater than -5.

c. j is greater than or equal to 4.

d. The speed limit, s, cannot exceed 55 mph.

e. 10 is less than or equal to x.

f. A number, x is at least 15.

g. A number, h is not greater than 4.

h. x is not more than 20.

i. A number, z, is negative.


j. To have a passing grade, g, must exceed a 70.

k. k is less than or equal to -3.

l. The total, t, is fewer than 8 items.

m. -2 is less than a number, n.

n. The time, t, on your quiz cannot exceed 20 minutes.

o. At most, 4 students, s, will fail the test.

99) Write an inequality for the graph below.








Homework

105) Write an inequality for each sentence below, and then graph the solutions of each inequality on a

number line.

a. w is greater than 7.

b. p is less than or equal to -1.

c. m is less than 5.

d. 11 is greater than or equal to k.

e. A number, f is positive.

f. The total, t is fewer than 4 items.

g. 4 is less than a number, n.

h. The speed limit, s, cannot exceed 25 mph.

i. A number c is at least 12.

j. w is not more than 50.


k. g is more than or equal to 8.

l. h is not less than -5.

m. The time, t for lunch cannot exceed 30 minutes.

n. At most, 25 students, s, will be in the class.

o. To have an A in class, g, must exceed a 92.








112) Explain how you know if the endpoint of the graph in an inequality should be an open dot or a

closed dot.

Simple Inequalities Involving Addition and Subtraction

Classwork

113) Solve, check and graph the following inequalities.

a. x + 5 > 10


b. x + 3 < -2

c. 7 > x + 11

d. x – 3 ≤ -5

e. x – 7 > 3

f. -2 + x ≥ -2

g. -9 ≤ x – 3

h. x + 0.5 < 4

i. -3.75 ≤ x – 1.25

j. 8.7 > x + 2.2

114) Write an inequality for each sentence below and then solve and check it.

a. The sum of w and nine is less than 18.

b. g decreased by 25 is at most five.

c. The difference of a number and six is no less than 15.

d. 14 is more than the sum of ten and a number.

e. 25 plus a number is at least 13.

115) Suppose you must maintain at least $500 in your checking account in order to have free

checking. Your balance is $542 and then you write a check for $57. How much do you need to

deposit in order to keep your free checking? Write an inequality and solve.

116) You need no more than 2,200 calories in a day. You had 650 calories at breakfast and 825

calories at lunch. At most, how many calories, c can you eat for dinner? Write an inequality and

solve.

Homework


a. x + 7 > -2

b. x + 3 < -3

c. -8 < x + 15

d. x – 4 ≤ 1

e. x – 1 > 6

f. -7 + x ≥ -11

g. -6 ≤ x – 2

h. x + 2.5 < 6

i. -5.5 ≤ x – 3.25

j. 7.9 > x + 4.4


a. The difference of a number and seven is at most 16.

b. 18 is less than a number plus 7

c. h decreased by 3 is more than 1.

d. 14 is greater than or equal to the sum of 18 and a number.

e. The sum of b and 22 is at least 6


119) Suppose you must maintain at least $500 in your checking account in order to have free

checking. Your balance is $612 and then you make a deposit of $79. How much can you

withdraw and still keep your free checking? Write an inequality and solve.

120) You need no more than 2,200 calories in a day. You had 720 calories at breakfast and plan on

having 1,000 calories at dinner. How many calories, c can you eat for lunch? Write an inequality

and solve.

Simple Inequalities Involving Multiplication and Division

Classwork


a. 5x > -25

b. -7x ≤ -21

c. 18 > 2x

d. 25x ≥ 100

e. -30 ≤ -6x

f. 10x < 0

g. 8x ≥ 24

h. 40 < -8x

i. 20x ≥ 30

j. 350 > -70x


a. 𝑥

5 ≥ 2

b. 𝑥

2 < 14

c. -3 ≤ 𝑥

−6

d. 𝑥

−9 > 1

e. 𝑥

−4 ≥ -3

f. 𝑥

3 ≤ 3

g. 0 ≤ 𝑥

8

h. -1 ≥ 𝑥

2.5


i. 𝑥

−1 < 2.2

j. 𝑥

−1.5 > -10


a. The product of r and 5 is no more than 55.

b. The quotient of v divided by -4 is greater than or equal to 2.

c. Half of d is greater than 40.

d. Twice a number is at most 24.

e. One-fourth of y is less than or equal to -12.

f. The product of -8 and x is no less than -64.

124) What happens to the inequality symbol when you do each of the following to both sides of an

inequality?

a. Multiply by a positive number

b. Divide by a positive number

c. Add a negative number

d. Subtract a negative number

e. Divide by a negative number

f. Multiply by a negative number

Homework


a. 4x ≤ -16

b. 32 ≤ 8x

c. -7x > 49

d. -5x < -55

e. 13x ≥ 0

f. 60 < 12x

g. 66 > -3x

h. -6x ≥ 360

i. -2x ≥ 17

j. 26 < 4x


a. 5 ≤ 𝑥

3

b. 𝑥

3 < -3

c. 𝑥

−8 ≥ 0


d. 𝑥

3 > 11

e. 4 ≤ 𝑥

−1

f. -4 ≥ 𝑥

−6

g. 𝑥

−4 ≥ -1.5

h. 𝑥

4 ≤ 12

i. 𝑥

−6 > -9

j. 𝑥

−2 < 3.3


a. Four times a number n is no more than 24.

b. One-third of m is greater than 9.

c. The product of -9 and g is at most 81.

d. Half of d is less than or equal to 16.

e. The quotient of v divided by -6 is less than 4.

f. The product of 7 and x is no less than -42.


Chapter Review

1) Edgar, Mufasa, and Ben shoveled the walkway of their houses. Edgar shoveled 3

8 of his

walkway, Mufasa shoveled 27%, and Ben shoveled 0.34. Who is the furthest along?

a. Edgar b. Mufasa c. Ben

2) Mike went shopping at the Nike outlet in Rehoboth Beach, DE. There is no additional

sales tax in the state of Delaware. He bought 5 T-shirts for $15 each and 2 pairs of

shorts. If his total was $125, how much did each pair of shorts cost?

a. $75

b. $50

c. $25

d. 12.50

3) Jason went to a carnival where he could go on all rides for a flat fee of $30 but he had to

pay $2 for each arcade game he played. Jason spent $44. How many arcade games did

he play?

a. 22 games

b. 37 games

c. 7 games

d. 15 games

4) Solve the following equations:

a. 2b = -94

b. r + 19 = -52

c. 9x + 6 = 33

d. 𝑚

4+ 8 = 14

e. 6(p + 2) = 30

f. 2

3(6𝑡 + 12) = 28

g. 4(𝑘 + 3) + 5𝑘 = 75

h. 3

5(ℎ + 10) = 9

i. 4

7(2𝑐 + 9) =

3

7

j. 4

5(3𝑛 + 2) =

1

2

5) Milan has 4 times as many baseball cards as Richard. Together they have 125 baseball

cards. How many cards does Milan have? How many cards does Richard have?

6) A rectangle is 6 inches longer than it is wide. The perimeter of the rectangle is 44 inches.

Write and solve an equation for the length and width of the rectangle.


7) You and a friend worked in the school store last week. You worked 4 hours less than

your friend. Together, you worked 36 hours. Write and solve an equation to find the total

number of hours you both worked.

8) A trail mix contains peanuts, raisins, and M&Ms. In the mix, the amount of peanuts is

three times the amount of M&Ms; and the amount of raisins is two times the amount of

M&Ms. There is a total of 96 items in the trail mix. Write and solve an equation for the

total number of each type of food in the trail mix.

9) Solve and graph each inequality on a number line.

a. 𝑥 + 9 > 17

b. 𝑥 − 13 ≤ 2

c. 5𝑥 ≥ −25

d. 𝑥

9> 3

e. 𝑥 + 9 < −6

f. 𝑥 − 2 > 2

g. −6𝑥 ≤ −42

h. 𝑥

−4≥ −1

10) Write an inequality for each diagram shown below.

a.

b.

c.

d.


11) Bob wants to go to the movies with his friends. The movie theater charges $8 per ticket.

Bob’s friends reserve $48.00 worth of tickets in advance. How many people in total can

attend the movie?

a) Identify the variable

b) Write an equation that includes the number of people attending the movie, the price of each ticket, and the total cost of the movie.

c) Solve the equation you wrote in part (b), make sure to show all steps.

12) Mary is 5 years older than Bob. If the sum of their ages is 39, write and solve an

equation to find their ages.

13) Consider the inequality 9x < 27.

Part A

Connor says that any value of x less than 18 makes the inequality true.

Use a specific example to disprove Connor’s statement.

Explain why your example disproves his statement.

Part B

Describe in words the values of x that make the inequality true. Explain your answer.


14) Chad complained to his friend that he had five equations to solve for homework.

Are all of the homework problems equations? Justify your answer.

Math Homework

1) 3x2 ∙ 2x4

2) 5 – 2x = 3x

3) 3(2x + 7)

4) 7x2 + 2x – 3x2 – 9

5) 2 = x + 2 3 6

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


Answer Key

1. a. Subtraction b. Addition c. Subtraction d. Multiplication e. Division

2. Michael’s method is better because he moved the number that was on the same side as the variable to get the variable by itself.

3. a. Addition b. Division c. Subtraction d. Division e. Multiplication

4. Lisa’s method is better because she

moved the number that was on the same side as the variable to get the variable by itself.

5. a. 13 b. -17 c. 42 d. 6 e. 42 f. 22 g. 128 h. 2 ½ i. -5 j. 72 k. 8 l. 6 m. 62 n. -10 o. 10.5 p. 4.5 q. 9

r. 53

s. 211

6. 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 o. 16 p. 7.48 q. 7

r. 54

s. 1252

7. 4 8. 27 9. -6 10. -8 11. -6 12. -19/14 13. 15/7 14. -21/8 15. 0 16. 24 17. 8 18. 1.5 19. -15.3 20. 4.2 21. 18 22. -10 23. 99 24. -5 25. -48 26. 1 27. 81 28. -6 29. -5 30. -2 31. 10 32. 3.1 33. 3.3 34. -16.8 35. 5 36. 88.2 37. 14 38. 1 39. 11 40. 14 41. 3 42. 1 43. 2 44. ½ 45. -9 46. 1 47. 2.5 48. 4 49. 6.1 50. 5.2


8

0

8

51. -8 52. 3 53. 3 54. -3/7 55. 13 56. 10 57. -9 58. 0.86 59. 11 60. 4.7 61. -1 62. 8.4 63. 6 64. 11 65. 14 66. 1 67. ½ 68. -6 69. -4 ½ 70. 2 71. 3 72. -8

73. 3.8 or 19

5

74. 3

75. −1. 5̅ or −14

9

76. 23 77. 3 78. 5 79. -4/5 80. -2 81. 7 82. 2 83. -2 84. 24

85. -3.25 or −13

4

86. -5 87. 2 88. a. 4 + 3x + x = 112; x = 85 b. 4w + 10 = 90; 20 c. 4(x – 3) = x – 27; -5 d. 3(21 + n) = 12; -17

89. Selina 90. 31 red, 93 blue 91. 7 games 92. Part A

4 ∙ 𝑛 + 84 = 132 Part B Each skirt cost $59.00

93. a. 6b + 36 = 84; 8 and 20 b. 4L – 26 = 90; 29 c. 6(n-9) = n – 19; 35 d. 56 + 8n = 16; -5

94. Jerrell 95. brother = 9, Lorena = 18 96. 3 sodas 97. Part A

2 ∙ 𝑛 + 36 = 76 Part B Each pair of sunglasses cost $7.00

98. a. y < 8

b. f > -5

c. j ≥ 4

d. s < 55

e. 10 < x

f. x ≥ 15

g. h < 4

h. x < 20

i. z < 0

j. g > 70

k. k < -3

l. t < 8

55

4

20

-3

4

10

15

-5

70


m. -2 < n

n. t < 20

o. 4 ≥ s

99. x>-2 100. x<7 101. x≥2 102. x<6 103. x<5 104. x≥-75

105.

a. w>7

b. p<-1

c. m<5

d. 11≥k

e. f>0

f. t<4

g. 4<n

h. s<25

i. x≥12

j. w<50

k. g≥8

l. h≥-5

m. t<30

n. 25≥s

o. g>92

106. x≥-6 107. x<-2 108. x<4 109. x>0 110. x>-10 111. x≥2.5 112. Opened: if possibility of being not equal

to, Closed: if possibility of equal to 113.

a. x>5

b. x<-5

c. -4≥x

d. x<-2

e. x>10

f. x≥0

g. -6<x

h. x<3.5

i. -2.5<x

j. 6.5>x

20

-2

4


114. a. w+9<18, w<9 b. g-25<5, g<30 c. x-6≥15, x≥21 d. 14>10+x, 4>x e. 25+x≥13, x≥-12

115. 542-57+x≥500, x≥15 116. 650+825+c<2200, c<725 117.

a. x>-9

b. x<-6

c. -23<x

d. x<5

e. x>7

f. x≥-4

g. -4<x

h. x<3.5

i. -2.25<x

j. 3.5>x

118. a. x-7<16, x<23 b. 18<x+7, 11<x c. h-3>1, h>4 d. 14≥18+x, -4≥x e. b+22≥6, b≥-16

119. 612+79-x≥500, 191≥x 120. 720+1000+c<2200, c<480 121.

a. x>-5

b. x≥3

c. 9>x

d. x≥4

e. 5≥x

f. x<0

g. x≥3

h. 5≥x

i. x≥3/2

j. 5<x

122. a. x≥10

b. x<28

c. 18≥x

d. x<-9

e. x<12

f. x<9

g. 0<x

h. -2.5≥x

i. x>-2.2


j. x<15

123. a. 5r<55, r<11 b. v/(-4) ≥2, v<-8 c. (d/2)>40, d>80 d. 2x<24, x<12 e. (y/4) <-12, <48 f. -8x≥-64, x<8

124. a. Nothing b. Nothing c. Nothing d. Nothing e. Change to the opp. inequality

sign f. Change to the opp. inequality

sign 125.

a. x<-4

b. 4<x

c. x<-7

d. x>11

e. x≥0

f. 5<x

g. -22<x

h. x<-60

i. x<8.5

j. 6.5<x

126. a. 15<x

b. x<-9

c. x<0

d. x>33

e. -4≥x

f. 24<x

g. x<6

h. x<48

i. x<54

j. x>-6.6

127. a. 4n<24, n<6 b. (m/3)>9, m>27 c. -9g<81, g≥-9 d. (d/2) <16, d<32 e. (v/-6)<4, v>-24 f. 7x≥-42, x≥-6

Chapter Review

1. a. Edgar 2. c. $25 3. c. 7 games 4. a. -47

b. -71 c. 3 d. 24

e. 3 f. 5 g. 7 h. 5


i. −41

2 j. −

11

24

5. Milan = 100, Richard = 25 6. 4w + 12 = 44; w = 8, L = 14 7. 2f – 4 = 36; friend = 20, you = 16 8. 6m = 96; M & Ms = 16, Raisins = 32, Peanuts = 48

9.

a. x > 8

b. x ≤ 15

c. x ≥ –5

d. x > 27

e. x < -15

f. x > 4

g. x ≥ 7

h. x ≤ 4

10.

a. x > 4 b. x ≤ -2 c. x < 6 d. x ≥ –7

11. a. t = tickets b. 8t = 48 c. 6 people

12. 2b + 5 = 39; Bob = 17, Mary = 22


13. Part A: Sample Answer: If x = 15, then 9(15) = 135 > 27, not less than 27. Since this value of x does not satisfy the inequality, Connor is incorrect. Part B: Sample Answer: The values of x that make the inequality true are any x-value less than 3. I found my answer by dividing both sides of the inequality by 9. I used this operation because it’s the inverse operation of multiplication, which is the operation shown between the 9 and x.

14. There are only 2 equations as only two of the questions have equal signs. The others are expressions.

Equations & Inequalities Chapter Questionscontent.njctl.org/courses/math/7th-grade/equations-inequalities-7th... · Equations & Inequalities Chapter Questions 1. What are inverse

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