Free Printable Solving Linear Inequalities

1.

x + 5 > 3

a)

x > -2

b)

x < 8

c)

x ≥ 2

d)

x ≥ 8

2.

-d - 2 ≥ -1

a)

d ≥ 3

b)

d > 1

c)

d < -1

d)

d ≤ -1

3.

b + 9 ≥ -3

a)

b ≤ -12

b)

b > 6

c)

b < -6

d)

b ≥ -12

4.

-7 -y > -2

a)

y ≥ 9

b)

y > 9

c)

y < -5

d)

y ≥ 5

5.

-9 - t > 9

a)

t ≥ 18

b)

t < '-18

c)

t < 0<br />

d)

t ≤ 0<br />

6.

-c - 3 < 2

a)

c ≥ 1

b)

c > '-5

c)

c ≥ 5

d)

c < 1

7.

-r - 7 < 1

a)

r < 8

b)

r ≥6

c)

r > '-8

d)

r ≤ -6

8.

-8 - w > 9

a)

w < '- 17

b)

w > 17

c)

w ≥ -17

d)

w ≤ 1

9.

-b - 4 ≤ -4

a)

b > 0

b)

b ≥ 0

c)

b < 8

d)

b ≤ 8

10.

-m + 8 < 3

a)

m > 5

b)

m > 11

c)

m ≥ -5

d)

m ≤ 11

11.

Which inequality symbol has a closed circle?

a)

<

b)

≤

12.

Which inequality symbol has a open circle?

a)

<

b)

≤

13.

Does the sign need to flip when solving?
-2x ≥ 22

a)

YES

b)

NO

14.

Solve:

-8b - 8 > 56

a)

b > 6

b)

b < -8

c)

b > -8

d)

b > 7/2

15.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

16.

-13t > 26

a)

t > -2

b)

t > 2

c)

t < 2

d)

t < -2

17.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

18.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

19.

X + 6 > 10

a)

X > 16

b)

X > -4

c)

X < -4

d)

X > 4

20.

-7x + 15 ≥ -20

a)

x ≥ -5

b)

x ≤ -5

c)

x ≥ 5

d)

x ≤ 5

21.

3(x-2)<2(x+9)

a)

x<24

b)

x>-24

c)

x<12

d)

x>18

22.

Which inequality symbol has a graph with an open (empty) circle?

a)

<

b)

≤

23.

Does the sign need to flip when solving?
-2x ≥ 22

a)

YES

b)

NO

24.

a)

A)

b)

B)

c)

C)

d)

D)

25.

a)

A)

b)

B)

c)

C)

d)

D)

26.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

27.

Solve and graph the inequality.
77 ≤ 5 + 8n

a)

A

b)

B

c)

C

d)

D

28.

Translate the following phrase: Jessica must be at least 48 inches to ride the roller coaster.

a)

j > 48

b)

j < 48

c)

j ≤ 48

d)

j ≥ 48

29.

Translate the following phrase: Tom can spend no more than 20 dollars on his mom's birthday present.

a)

t > 20

b)

t < 20

c)

t ≤ 20

d)

t ≥ 20

30.

Translate the following phrase: You and your friends ate more than 8 slices of pizza at the party.

a)

x > 8

b)

x < 8

c)

x ≤ 8

d)

x ≥ 8

31.

Translate the following phrase: Bob spends less than 5 hours on homework each night.

a)

b > 5

b)

b < 5

c)

b ≤ 5

d)

b ≥ 5

32.

Translate the following phrase: Edith must read for a minimum of 20 minutes every night.

a)

e > 20

b)

e < 20

c)

e ≥ 20

d)

e ≤ 20

33.

Translate the following phrase: All students must get at least a 65% for the year in order to pass math.

a)

s = 65

b)

s > 65

c)

s ≥ 65

d)

s ≤ 65

34.

Translate the following phrase: Grace has $45 at most in her purse on a daily basis

a)

g < 45

b)

g > 45

c)

g ≤ 45

d)

g ≥ 45

35.

You need to save a minimum of $1200 to purchase your new laptop. If you already have saved $400 and make 11 per hour, h, at your job, which inequality could be use to solve to determine how many hours you need to work to save enough money.

a)

11h + 1200 ≥ 400

b)

11h + 400 < 1200

c)

11h + 400 > 1200

d)

11h + 400 < 1200

36.

Pick the correct letter for the graph of:

6 > x

Hint: You need to REWRITE the inequality with the variable first.

a)

A

b)

B

c)

C

d)

D

37.

$x+3<7$ Solve the inequality

a)

$x<4$

b)

$x=4$

c)

$x<10$

d)

$x=10$

38.

Solve the inequality $x+5\ge1$

a)

$x>-4$

b)

$x\ge-4$

c)

$x\ge6$

d)

$x=-4$

39.

Solve the inequality $2x\le12$

a)

$x<6$

b)

$x\le6$

c)

$x\le24$

d)

$x=6$

40.

Solve the inequality $\frac{x}{3}>2$

a)

$x>6$

b)

$x\ge6$

c)

$x>5$

d)

$x\ge5$

41.

Solve the inequality $5x-7<3$

a)

$x=2$

b)

$x\le2$

c)

$x<2$

d)

$x<\frac{-4}{5}$

42.

Solve the inequality $3x+7\ge1$

a)

$x\ge2$

b)

$x\ge\frac{8}{3}$

c)

$x\le2$

d)

$x\ge-2$

43.

Solve the inequality $\frac{x}{4}>-3$

a)

$x>-12$

b)

$x>12$

c)

$x=12$

d)

$x=-12$

44.

Solve the inequality $3x+4<16$

a)

$x<4$

b)

$x<\frac{20}{3}$

c)

$x=4$

d)

$x=\frac{20}{3}$

45.

Solve the inequality $\frac{x}{2}+4\le6$

a)

$x\le5$

b)

$x\le20$

c)

$x\le1$

d)

$x\le4$

46.

Solve the inequality $3\left(x+4\right)\le9$

a)

$x\le2$

b)

$x\le-1$

c)

$x\le7$

d)

$x\le27$

47.

Solve the inequality $5<3x-1<14$

a)

$2<x<3$

b)

$x<2$

c)

$x<3$

d)

$\frac{4}{3}<x<\frac{14}{3}$

48.

Solve.

|x + 4| < 5

a)

x < -9 or x > 1

b)

-9 < x < 1

c)

x < 9 or x > -1

d)

-1 < x < 9

49.

Solve.
|y - 4| ≥ 8

a)

y ≤ -4 or y ≥ 12

b)

-4 ≤ y ≤ -12

c)

y ≤ 4 or y ≥ -12

d)

-12 ≤ x ≤ 4

50.

Solve.
|y - 1| ≤ 6

a)

-7 ≤ y ≤ 5

b)

y ≤ -7 or y ≥ 5

c)

-5 ≤ y ≤ 7

d)

y ≤ -5 or y ≥ 7

51.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

52.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

53.

Solve.

3|d - 4| ≥ 12

a)

d = -8 or d = 0

b)

no solution

c)

d ≥ 8 or d ≤ 0

d)

d = 40 or d = 32

54.

Solve.

|d + ⅔| + ¾ < 0

a)

no solution

b)

d > -9 and d < ½

c)

d > -¾ and d < 9

d)

d < -1/12 and d > -7/12

55.

Solve.
|5x + 7| < 22

a)

x < -5 ⅘ or x > 3

b)

-5 ⅘ < x < 3

c)

-3 < x < 5 ⅘

d)

x < -3 or x > 5 ⅘

56.

Solve.

|4v + 12| ≥ 6

a)

v ≤ -4.5 or v ≥ -1.5

b)

-4.5 ≤ v ≤ -1.4

c)

-1.5 ≤ v ≤ 4.5

d)

v ≤ -1.5 or v ≥ 4.5

57.

Solve.

3|2d + 9| + 13 > 10

a)

d > 5 or d < -1

b)

d < -4 or d > 5

c)

No Solution

d)

All real numbers

58.

Which interval notation is represented by the graph?

a)

$\left(-20,\ -10\right)$

b)

$\left[-20,\ -10\right]$

c)

$\left(-20,\ -10\right]$

d)

$\left[-20,\ -10\right)$

59.

Which interval notation is represented by the graph?

a)

$\left(-16,\ 2\right)$

b)

$\left[-16,\ 4\right]$

c)

$\left(-\infty,-16\right)\cup\left(2,\ \infty\right)$

d)

( $-\infty,-16$ ] , [ $2,\infty$ )

60.

Identify the absolute value inequality that would generate the given graph.

a)

$\left|x+12\right|>5$

b)

$\left|x+12\right|\ge5$

c)

$\left|x+12\right|<5$

d)

$\left|x+12\right|\le5$

61.

Identify each value that is a solution to the indicated inequality. $\left|x\right|-2\le0$

a)

$-4$

b)

$-2$

c)

$0$

d)

$1$

e)

$4$

62.

Solve.

|x + 4| < 5

a)

x < -9 or x > 1

b)

-9 < x < 1

c)

x < 9 or x > -1

d)

-1 < x < 9

63.

Solve.
|y - 4| ≥ 8

a)

y ≤ -4 or y ≥ 12

b)

-4 ≤ y ≤ -12

c)

y ≤ 4 or y ≥ -12

d)

-12 ≤ x ≤ 4

64.

Solve.
|y - 1| ≤ 6

a)

-7 ≤ y ≤ 5

b)

y ≤ -7 or y ≥ 5

c)

-5 ≤ y ≤ 7

d)

y ≤ -5 or y ≥ 7

65.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

66.

Solve.
|3c - 4| < 12

a)

-2 2/3 < c < 5 1/3

b)

c < -5 1/3 or c > 2 2/3

c)

c < 5 1/3 or c > -2 2/3

d)

-5 1/3 < c < 2 2/3

67.

Solve.

3|d - 4| ≥ 12

a)

d = -8 or d = 0

b)

no solution

c)

d ≥ 8 or d ≤ 0

d)

d = 40 or d = 32

68.

Solve.

|d + ⅔| + ¾ < 0

a)

no solution

b)

d > -9 and d < ½

c)

d > -¾ and d < 9

d)

d < -1/12 and d > -7/12

69.

Solve.
|5x + 7| < 22

a)

x < -5 ⅘ or x > 3

b)

-5 ⅘ < x < 3

c)

-3 < x < 5 ⅘

d)

x < -3 or x > 5 ⅘

70.

Solve.

|4v + 12| ≥ 6

a)

v ≤ -4.5 or v ≥ -1.5

b)

-4.5 ≤ v ≤ -1.4

c)

-1.5 ≤ v ≤ 4.5

d)

v ≤ -1.5 or v ≥ 4.5

71.

Solve.

3|2d + 9| + 13 > 10

a)

d > 5 or d < -1

b)

d < -4 or d > 5

c)

No Solution

d)

All real numbers

72.

Which interval notation is represented by the graph?

a)

$\left(-20,\ -10\right)$

b)

$\left[-20,\ -10\right]$

c)

$\left(-20,\ -10\right]$

d)

$\left[-20,\ -10\right)$

73.

Which interval notation is represented by the graph?

a)

$\left(-16,\ 2\right)$

b)

$\left[-16,\ 4\right]$

c)

$\left(-\infty,-16\right)\cup\left(2,\ \infty\right)$

d)

( $-\infty,-16$ ] , [ $2,\infty$ )

74.

Identify the absolute value inequality that would generate the given graph.

a)

$\left|x+12\right|>5$

b)

$\left|x+12\right|\ge5$

c)

$\left|x+12\right|<5$

d)

$\left|x+12\right|\le5$

75.

Identify each value that is a solution to the indicated inequality. $\left|x\right|-2\le0$

a)

$-4$

b)

$-2$

c)

$0$

d)

$1$

e)

$4$

76.

What is the solution of the inequality?

a)

a < -2

b)

a > 5

c)

a > 2

d)

a < 2

77.

a)

Yes, dividing both sides by 10

b)

No because Distributive property is the only way of solving it

c)

Yes, dividing by 2 each side

d)

Yes by multiplying the parenthesis by 2

78.

Solve the inequality. Don't forget to check your solution set.
12 ≥ 15 - 6y

a)

y ≤ ½

b)

y ≤ 2

c)

y ≥ ½

d)

y ≥ 2

79.

Solve:
3(x - 2) < 2(x + 9)

a)

x<24

b)

x>12

c)

x<12

d)

x>24

80.

Solve. 3(k-5) + 9k ≥ -3

a)

k ≥ 0

b)

k ≤ -1

c)

k≥ 1

d)

k≥ 2

81.

Which graph represents x<-2 or x>3?

a)

Graph 1

b)

Graph 2

c)

Graph 3

82.

What inequality is being represented?

a)

5<x<9

b)

5≤x≤9

c)

5<x≤9

d)

5≤x<9

83.

Solve and graph:

a)

A

b)

B

c)

C

d)

D

84.

Write an inequality for Graph 3.

a)

x ≤ -2 AND x > 5

b)

x ≤ -2 OR x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x < 5

85.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

86.

What inequality is graphed?

a)

x > 2 and x < 4

b)

x ≥ 2 and x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

87.

Solve:
3 | 2x + 7| + 7 < 4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

88.

Solve:
|x + 4| - 8 > 2

a)

x > 6 and x < 10

b)

x > 6 or x < -14

c)

all real numbers

d)

no solution

89.

Solve the absolute Value inequality and graph.

a)

A

b)

B

c)

C

d)

D

90.

Is the line for the inequality

f(x) ≥|x+3|- 9 going to solid or dotted?

a)

Dotted

b)

Solid

c)

I don't know

91.

What inequality is graphed?

a)

x > 2 and x ≤ -3

b)

x > 2 and x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

92.

Write an inequality for Graph 4.

a)

-2 < x < 5

b)

x < -2 or x > 5

c)

x ≥ -2 OR x < 5

d)

-2 ≤ x ≤ 5

93.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

94.

Solve the inequality:

2x + 1 > 9 or x - 4 < 6

a)

No solution

b)

4 < x < 10

c)

x > 4 or x < 10

d)

All real numbers

95.

Solve the inequality:

-3x + 7 >25 AND -9 - 5x < -39

a)

-6 < x < 6

b)

No Solution

c)

x < -6

d)

x > 6

96.

Solve the inequality:

9x - 6 > 66 AND 4x + 8 > 24

a)

No Solution

b)

x > 8

c)

x > 4

d)

4 < x < 8

97.

Solve the inequality:

x - 10 > -7 OR 8 - 2x < 6

a)

x > 3

b)

All Real Numbers

c)

x > 1

d)

x < 1 or x > 3

98.

Solve.

-5\left|x-4\right|>-20

a)

x < 8 and x > 0

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

99.

Solve.

-5\left|n+4\right|<-15

a)

n > 1 or n < -7

b)

n > -1 or n < -7

c)

-7 < n < -1

d)

no solution

100.

Which compound inequality involves <, ≤ when solving absolute value inequalities?

a)

and

b)

or

101.

Which compound inequality involves >,≥ when solving absolute value inequalities?

a)

and

b)

or

102.

Solve:

3\left|2x+7\right|-7<-4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

103.

Which of the graphs represents the linear inequality $y>\frac{1}{2}x+3$ ?

a)

b)

c)

d)

104.

Which of the following linear inequalities represents the graph?

a)

$y\ge3x-5$

b)

$y\ge\frac{1}{3}x-5$

c)

$y\le-\frac{1}{3}x-5$

d)

$y>\frac{1}{3}x+5$

105.

Which of the following linear inequalities represents the graph?

a)

$y\ge3$

b)

$x\ge3$

c)

$y\le3$

d)

$y<3$

106.

Which of the following linear inequalities represents the graph?

a)

$x\ge2$

b)

$x\ge-2$

c)

$y\ge-2$

d)

$y>-2$

107.

When graphing a linear inequality, < and > signs would require you to draw...

a)

a solid line

b)

a dotted line

108.

When graphing a linear inequality, $\le$ and $\ge$ signs would require you to draw...

a)

a solid line

b)

a dotted line

109.

Which of the graphs represents the linear inequality $y\le-x-4$ ?

a)

b)

c)

d)

110.

Are the points on the boundary line part of the solution set or not?

a)

Yes, they are part of the solution set

b)

No, they are NOT part of the solution set

111.

Determine whether point A is a solution to the linear inequality that is shown.

a)

Yes

b)

No

c)

Sometimes

112.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, -10)

c)

(-1, 5)

d)

(5, 20)

113.

Solve and write your answer in interval notation.

a-6\le15+8a

a)

[-3, ∞)

b)

(-∞, -3]

c)

(3, ∞)

d)

(-3, ∞]

114.

Solve and write your answer in interval notation.

28-7x\le-4\left(-7x-7\right)

a)

(0, ∞)

b)

[0, ∞)

c)

(0, ∞]

d)

(-∞, 0]

115.

Express the following in Interval Notation

-8 ≤ x < 8

a)

[-8, 8]

b)

[-8,8)

c)

(-8, 8]

d)

(-8, 8)

116.

Express the following interval as an inequality:

[3, 5]

a)

3 ≤ x ≤ 5

b)

3 < x ≤ 5

c)

3 ≤ x < 5

d)

3 < x < 5

117.

Express the following interval as an inequality:

(-7, 15]

a)

-7 ≤ x ≤ 15

b)

-7 < x ≤ 15

c)

-7 ≤ x < 15

d)

-7 < x < 15

118.

What interval notation does the number line graph represent?

a)

[∞, -5)

b)

(∞, -5)

c)

[-5, ∞)

d)

(-5, ∞)

119.

Solve the following inequality. Express the solution in interval notation:

5z - 2 < 13 + 2z

a)

(5, ∞)

b)

(-∞, 5)

c)

(1, ∞)

d)

(-∞, 1)

120.

Which is a solution of...

5(v + 3) > 10v - 10

a)

(-∞, 5)

b)

(5, ∞)

c)

(-5, ∞)

d)

(-∞, -5)

121.

Solve the following inequality:
$5-\left(4x-5\right)\le30$

a)

x ≤ -5

b)

x < 10

c)

x ≥ -5

d)

x ≥ 10

122.

Solve

-2x+3\left(-4x+6\right)\le116

a)

x ≤ -7

b)

x ≥ 29

c)

x ≥ -7

d)

x ≤ 29

123.

Solve 5( 6 + 3r) + 7 ≥ 127. Express the solution in interval notation.

a)

(-∞, 6]

b)

[6, ∞)

c)

(-∞, -6]

d)

[-6, ∞)

124.

Solve:
|x + 3| > 8

a)

x > 5 or x < -11

b)

x > 5

c)

all real numbers

d)

no solution

125.

Solve:

3 | 2x + 7| - 7 < -4

a)

x < -3 or x > -5/3

b)

-4 < x < -3

c)

all real numbers

d)

no solution

126.

Solve:
3 | 2x + 7| + 7 < 4

a)

x < -3 and x > -5/3

b)

x < -3 and x > -4

c)

all real numbers

d)

no solution

127.

Solve.

-5|x - 4| > -20

a)

0 < x < 8

b)

x > 8 or x < 0

c)

all real numbers

d)

no solution

128.

Solve the inequality below. Express the solution in interval notation.

6 - 2|m -3| > -4

a)

$\left(-8,2\right)$

b)

$\left(-\infty,-8\right)or\left(2,\infty\right)$

c)

$\left(-\infty,-2\right)or\left(8,\infty\right)$

d)

$\left(-2,8\right)$

129.

Solve the following inequality:

\frac{\left|6a+3\right|}{3}>2

a)

no solution

b)

$a>\frac{-1}{6}or\ a<\frac{-5}{6}$

c)

$a>\frac{1}{2}\ or\ a<\ \frac{-3}{2}$

d)

all real numbers

130.

3x - 4 < -13 or 7x + 1 > 22

a)

All Real numbers

b)

x > 3 and x > -9

c)

The answer is not listed

d)

x < -3 or x > 3

131.

Solve the following inequality. Express the solution in interval notation:

-3\le2x-1\le5

a)

[-1, 3]

b)

(-1, 3)

c)

(1, 3)

d)

[1, 3]

132.

What is the interval notation for the solution graphed here?

a)

[-2, 5)

b)

(-2, 5]

c)

$\left(-\infty,-2\right]\ or\ \left(5,\infty\right)$

d)

$\left[-2,-\infty\right)\ or\ \left(5,\ \infty\right)$

Solving Linear Inequalities

Total questions: 132

Worksheet time: 11hrs 4mins

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