Free Printable Inequalities

1.

To qualify for an award, a student volunteers no less than 5 hours each week at the local hospital. Write an inequality that represents how many hours the student volunteers each week.

a)

X < 5

b)

X > 5

c)

X ≥ 5

d)

X ≤ 5

2.

Solve the following inequality:
-4x + 14 ≤ 54

a)

x ≥ -10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

3.

Match the graph with the given solution.

a)

A

b)

B

c)

C

d)

D

4.

Solve and then match the correct solution & graph.

a)

A

b)

B

c)

C

d)

D

5.

When graphing an inequality, you use an OPEN dot when you use which symbol?

a)

<, >

b)

≤, ≥

c)

≤, <

d)

≥, >

6.

When you graph an inequality, you used a CLOSED dot when you use which symbols?

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

7.

a)

x is less than or equal to -2

b)

x < -2

c)

-2 < x

d)

x is greater than -2

8.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

9.

x is no more than 13

a)

x < 13

b)

x > 13

c)

x ≥ 13

d)

x ≤ 13

10.

Which inequality matches the graph?

a)

x<3

b)

x>3

c)

x<3

d)

x>3

11.

Which scenario could be represented by the graph?

a)

The temperature is less than -1 degree.

b)

The temperature is more than -1 degree.

c)

The temperature is at most -1 degree.

d)

The temperature is at least -1 degree.

12.

You must spend at least $10 at the grocery store to get a free reusable shopping bag. Which inequality represents the amount you need to spend to get a free shopping bag?

a)

x<10

b)

x>10

c)

x>10

d)

x<10

13.

When the following inequality is graphed, what will it look like?

"Kelsey has at most 10 dollars"

a)

open circle

b)

closed circle

14.

When the following inequality is graphed, what will it look like?

"Alex will spend less than 35 minutes playing video games"

a)

open circle

b)

closed circle

15.

a)

greater than

b)

less than

c)

less than or equal to

d)

greater than or equal to

16.

a)

greater than

b)

less than

c)

less than or equal to

d)

greater than or equal to

17.

a)

greater than

b)

less than

c)

less than or equal to

d)

greater than or equal to

18.

a)

greater than

b)

less than

c)

less than or equal to

d)

greater than or equal to

19.

8x ≥ -32

a)

x ≥ -4

b)

x ≥ 4

c)

x ≤ -4

d)

x ≥ 4

20.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

21.

4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

22.

7b - 3 < 11

a)

b < 2

b)

84 > b

c)

b > 2

d)

b < 84

23.

a)

x is less than or equal to -2

b)

x < -2

c)

-2 < x

d)

x is greater than -2

24.

x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

25.

10 ≥ x - 3

a)

x ≤ 13

b)

x ≥ 13

c)

x ≤ 7

d)

x ≥ 7

26.

-12y - 11 < 49

a)

y < -5

b)

y > - 5

c)

y > 5

d)

y < 5

27.

-3r + 10 < -2

a)

r < -8/3

b)

r > -8/3

c)

r > 4

d)

r < 4

28.

-3 + x ≤ -11

a)

x ≤ -8

b)

x ≤ 8

c)

x ≥ -8

d)

x ≥ 8

29.

2x < -3x + 15

a)

x > 3

b)

x > 15

c)

x < 3

d)

x < 15

30.

6x - 4 ≥ 26

a)

x ≥ 3.67

b)

x ≥ 5

c)

x < 5

d)

x ≤ 5

31.

3x - 2 < 13

a)

x > 3.67

b)

x > 5

c)

x < 5

d)

x < 3.67

32.

2x - 3 ≥ 4x - 1

a)

x ≤ -1

b)

x ≥ -1

c)

x ≤ 1

d)

x ≥ 1

33.

4x - 3 < -1x + 12

a)

x > 3

b)

x < 3

c)

x < 5

d)

x > 5

34.

.5(x - 8) < 2

a)

x > 20

b)

x < 20

c)

x > 12

d)

x < 12

35.

-1(2x + 4) ≥ 6

a)

x ≤ -5

b)

x ≥ -5

c)

x ≤ -1

d)

x ≥ -1

36.

-2x + 2 > 3x - 8

a)

x > -9

b)

x > 2

c)

x < -9

d)

x < 2

37.

What inequality is graphed here?

a)

x > 1

b)

x ≥ 1

c)

x < 1

d)

x ≤ 1

38.

3(x - 3) ≤ 2(x + 2)

a)

x ≤ -5

b)

x ≥ 5

c)

x ≥ 13

d)

x ≤ 13

39.

Translate: 5 times a number is at least 60.

a)

5x < 60

b)

5x > 60

c)

5x ≤ 60

d)

5x ≥ 60

40.

Translate:

A number increased by 4 is no more than -18.

a)

x + 4 < -18

b)

x + 4 > -18

c)

x + 4 ≤ -18

d)

x + 4 ≥ -18

41.

Translate:

Twice a number is smaller than 42.

a)

2x < 42

b)

2x > 42

c)

2x ≤ 42

d)

2x ≥ 42

42.

Solve
-9h > (-63)

a)

h < 7

b)

h > 7

c)

h < -7

d)

h > -7

43.

Solve:
8m - 9 > 71

a)

m > 10

b)

m > 1

c)

m < 1

d)

m > -48

44.

15 + 7x ≥ 29

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x > 2

45.

Four times a number, increased by 6 is greater than 22. Which inequality models this scenario?

a)

4x - 6 > 22

b)

4x + 6 < 22

c)

4x + 6 ≥ 22

d)

4x + 6 > 22

46.

-2x + 3(-4x + 6) ≤116

a)

x ≤ -7

b)

x ≥ 29

c)

x ≥ -7

d)

x ≤ 29

47.

Which graph represents the inequality 2x + 3 < 7

a)

b)

c)

d)

48.

You flip an inequality symbol when you...

a)

subtract

b)

multiply and divide only

c)

multiple by a negative number

d)

multiple or divide by a negative number

49.

Do you flip the sign?
-3x + 2 ≤ 22

a)

YES

b)

NO

50.

Which could be a possible solution?

a)

8

b)

18

c)

16

d)

22

51.

Solve:

a)

x < 24

b)

x < 3

c)

x > 24

d)

x < 10.3333....

52.

6x + 2 + 6x < 14

a)

x < 1

b)

x > 1

c)

x < -1

d)

x > -1

53.

Solve the inequality

4(5x + 2) ≤ 28

a)

x ≤ 1

b)

x ≥ 1

c)

x ≤ 8

d)

x ≥ 8

54.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

55.

Solve:
7(x + 3) < 5x + 13

a)

x>-4

b)

x < 17

c)

x<-4

d)

x > -17

56.

28 − k ≥ 7(k − 4)

a)

k ≥ -7

b)

k ≤ -7

c)

k ≥ 7

d)

k ≤ 7

57.

-138 ≥ -6(6b − 7)

a)

b ≤ 5

b)

b ≤ -5

c)

b ≥ 5

d)

b ≥ -5

58.

a − 6 ≤ 15 + 8a

a)

a ≤ -3

b)

a ≥ -3

c)

a ≤ 3

d)

a ≥ 3

59.

-2(5 + 6n) < 6(8 − 2n)

a)

no solution

b)

infinite solution

c)

x < 0

d)

x > 0

60.

Your taxi fare is $2.50 per mile, plus a $5 fee. You cannot exceed $20. Which inequality models this scenario?

a)

5x + 2.50 ≤ 20

b)

2.50x + 5 < 20

c)

2.50x + 5 ≤ 20

d)

7.50x < 20

61.

Solve: -2x ≤ 14

a)

x ≤ 7

b)

x ≤ -7

c)

x ≥ 7

d)

x ≥ -7

62.

Solve

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

63.

Solve

28 − k ≥ 7(k − 4)

a)

k ≥ -7

b)

k ≤ -7

c)

k ≥ 7

d)

k ≤ 7

64.

Solve

3x − (2 + 6x) ≤ -32

a)

x ≥ 10

b)

x< -10

c)

x ≥ -10

d)

All real numbers

Inequalities

Total questions: 64

Worksheet time: 5hrs 20mins

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