Free Printable Solving Inequalities

1.

x + 5 > 7

a)

x > -2

b)

x > 2

c)

x > 12

d)

x > -12

2.

-4 + y < -8

a)

y < 4

b)

y < -12

c)

y < -4

d)

y < 12

3.

Solve
(n/3) > -20

a)

n > 60

b)

n < -17

c)

n > -60

d)

n < -23

4.

Solve
-9h > (-63)

a)

h < 7

b)

h > 7

c)

h < -7

d)

h > -7

5.

4x + 1 > 13

a)

x > 48

b)

x < 3

c)

x > 3.5

d)

x > 3

6.

-9x + 7 ≥ 25

a)

x ≥ -3.6

b)

x ≤ 2

c)

x ≥ -2

d)

x ≤ -2

7.

Solve the following inequality. Show your algebraic work!

a)

b > 6

b)

b < -4

c)

b > 1

d)

b < -12

8.

-1(2x + 4) ≥ 6

a)

x ≤ -5

b)

x ≥ -5

c)

x ≤ -1

d)

x ≥ -1

9.

Solve the following inequality. Show your algebraic work!

a)

x > -2

b)

x > 1

c)

x > 3

d)

x < 4

10.

What inequality does the number line graph represent?

a)

x > 5

b)

x < −5

c)

x ≥ 5

d)

x ≥ −5

11.

Match the graph with its inequality.

a)

a > 11

b)

a < 11

c)

a ≥ 11

d)

a ≤ 11

12.

4x - 10 ≤ 22

a)

x ≤ 8

b)

x ≥ 8

c)

x ≤ 3

d)

x ≥ 3

13.

15 + 7x ≥ 29

a)

x ≥ 2

b)

x ≥ -2

c)

x ≤ 2

d)

x > 2

14.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

15.

-2x + 3(-4x + 6) ≤116

a)

x ≤ -7

b)

x ≥ 29

c)

x ≥ -7

d)

x ≤ 29

16.

4x - 3 < -1x + 12

a)

x > 3

b)

x < 3

c)

x < 5

d)

x > 5

17.

-2x + 2 > 3x - 8

a)

x > -9

b)

x > 2

c)

x < -9

d)

x < 2

18.

3(x - 3) ≤ 2(x + 2)

a)

x ≤ -5

b)

x ≥ 5

c)

x ≥ 13

d)

x ≤ 13

19.

When graphing do you use an open or closed circle for > ?

a)

Open

b)

Closed

20.

Which graph represents the inequality 2x + 3 < 7

a)

b)

c)

d)

21.

Penelope is going to the carnival to ride the rides. It costs $20 to get into the carnival and ride tickets are $0.50 each. Write an equation that represents this scenario if she can spend no more than $35 in all.

a)

.50x + 20 ≥ 35

b)

.50x < 35

c)

.50 + 20x ≤ 35

d)

.50x - 20 = 35

22.

A limo driver needs to make more than $450 in one day. He charges a rental fee of $375 and $0.85 per mile. What inequality represents the number of miles, x, he would have to drive to reach his goal?

a)

0.85x + 375 > 450

b)

0.85x + 375 < 450

c)

0.85 + 375x > 450

d)

0.85 + 375x < 450

23.

Do you flip the sign?
-3x + 2 ≤ 22

a)

YES

b)

NO

24.

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

25.

Does the sign need to flip when solving?
8y < (-40)

a)

YES

b)

NO

26.

solve 3 < -5n + 2n

a)

n < -1

b)

n ≤ -1

c)

n > -4

d)

n < -3

27.

Which could be a possible solution?

a)

8

b)

18

c)

16

d)

22

28.

Solve:

a)

x < 24

b)

x < 3

c)

x > 24

d)

x < 10.3333....

29.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-1 < x < 3

c)

1 < x < 3

d)

1 ≤ x ≤ 3

30.

-3 < x + 6 ≤ 5

a)

-9< x or x≤ -1

b)

All Real numbers

c)

-9< x and x≤ -1

d)

-10< x and x≤ -7

31.

Does the given value make the inequality true? x + 9 > 21, when x = 15

a)

True

b)

Not True

32.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

33.

What inequality is graphed here?

a)

x > 1

b)

x ≥ 1

c)

x < 1

d)

x ≤ 1

34.

-2x + 2 > 3x - 8

a)

x > -9

b)

x > 2

c)

x < -9

d)

x < 2

35.

Translate: 5 times a number is at least 60.

a)

5x < 60

b)

5x > 60

c)

5x ≤ 60

d)

5x ≥ 60

36.

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

37.

Translate:

Twice a number is smaller than 42.

a)

2x < 42

b)

2x > 42

c)

2x ≤ 42

d)

2x ≥ 42

38.

Do you flip the sign?
-3x + 2 ≤ 22

a)

YES

b)

NO

39.

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

40.

Select all of the values that are solutions to x͕ ≥ -8.

a)

-8.01

b)

8.01

c)

8

d)

-8

41.

When graphing do you use an open or closed circle for > ?

a)

Open

b)

Closed

42.

When graphing do you use an open or closed circle for < ?

a)

Open

b)

Closed

43.

You spend at least 50 minutes practicing football each day. You spent 28 minutes practicing this morning. You want to practice twice as long in the afternoon. How long will you need to practice for?

a)

28 + 2x < 50

b)

28 + 2x < 50

c)

28 + 2x > 50

d)

28 + 2x > 50

44.

10 - 3x < 16

a)

x < -2

b)

x > -2

c)

x < 2

d)

x > 2

45.

84 - 4x ≤ 52

a)

x > 8

b)

x < 8

c)

x > 8

d)

x < 8

46.

Which graph represents x > 2

a)

b)

c)

d)

47.

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

48.

Which is the solution of
-4 - 6m > -9m + 8?

a)

m < -4

b)

m > 4

c)

m < 15

d)

m > 36

49.

Which inequality matches the graph?

a)

A

b)

B

c)

C

d)

D

50.

When graphing an inequality, what does a closed circle mean?

a)

The number is not included in the list of answers.

b)

The number is included in the list of answers.

51.

Which numbers are possible solutions to the inequality... (SELECT ALL THAT APPLY)

-5x + 10 < 30

a)

0

b)

100

c)

-100

d)

-3

e)

-4

52.

Which numbers are possible solutions to the inequality... (SELECT ALL THAT APPLY)

x+6x≤2(2+3x)

a)

4

b)

100

c)

5

d)

0

e)

-100

53.

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

a)

≤, ≥

b)

<, >

54.

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

a)

<, >

b)

≤, ≥

55.

In an equation or inequality, you want to get the variable...

a)

on one side

b)

to disappear

c)

isolated (by itself)

56.

"At most" and "No more than" are both clue words for...

a)

<

b)

>

c)

≤

d)

≥

57.

Write an inequality for this situation:
You are driving, and the maximum speed limit is 55.

a)

s < 55

b)

s > 55

c)

s ≤ 55

d)

s ≥ 55

58.

6 + 2h > 30

a)

h < 24

b)

18 > h

c)

h > 12

d)

h < -12

59.

At Least

a)

<

b)

>

c)

≤

d)

≥

60.

No Fewer Than

a)

<

b)

>

c)

≤

d)

≥

61.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

62.

Do I need to flip my sign?
3x ≥ 12

a)

Yes

b)

No

63.

Write the phrase as an expression.
twice a number x plus 8 is greater than 12

a)

2 + 8x < 12

b)

2x + 8 > 12

c)

2(x+8) ≠ 12

d)

8(2+x)

64.

-2(x+2) < 14

a)

x < - 5

b)

x > -5

c)

x < -9

d)

x > -9

65.

What are two solutions to
x < 8?

a)

8.6, 7.9

b)

11, 16

c)

0.8, 5.9

d)

12, 7.1

66.

Match:
The postal scale will weigh a maximum of 50 lbs.

a)

p < 50

b)

p > 50

c)

p ≤ 50

d)

p ≥ 50

67.

Match:
You must be at least 48 inches tall to ride the bumper cars.

a)

h < 48

b)

h > 48

c)

h ≤ 48

d)

h ≥ 48

68.

Write an inequality
Bob needs at most 10 to go to the movies

a)

x<10

b)

x>10

c)

x≤10

d)

x≥10

69.

Which sentence represents m > 41?

a)

Mary’s points, m, totaled more than 41

b)

Calvin ran no less than 41 miles, m

c)

The temperature, m, was less than 41°F

d)

The magazines’ cost, m, was not more than $41.

70.

-8x < 48

a)

x < -6

b)

x > -6

c)

x < 6

d)

x > 6

71.

9 ≥ -2m + 2 − 3

a)

m ≤ 5

b)

m ≤ -5

c)

m ≥ -5

d)

m ≥ 5

72.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

73.

You want to spend at most $1200 on a new laptop. If you make a $400 down payment, then pay the same amount every month for 12 months. Which Inequality could be use to solve to find out how much you can pay each month.

a)

12x + 1200 > 400

b)

12x + 400 < 1200

c)

12x + 400 > 1200

d)

12x + 400 < 1200

74.

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

75.

-3 − 6(4x + 6) > -111

a)

x > 3

b)

x < 3

c)

x < -3

d)

x > -3

76.

Solve the inequality

a)

x ≤ 2

b)

x ≤ -2

c)

x ≥ 2

d)

x ≥ -2

77.

Solve.
(2x - 3) / 4 = 9

a)

x = 24

b)

x = 12

c)

x = 17.5

d)

x = 19.5

78.

6x + 2 + 6x < 14

a)

x < 1

b)

x > 1

c)

x < -1

d)

x > -1

79.

-138 ≥ -6(6b − 7)

a)

b ≤ 5

b)

b ≤ -5

c)

b ≥ 5

d)

b ≥ -5

80.

-p − 4p > -10

a)

p > -2

b)

p > 2

c)

p < -2

d)

p < 2

81.

I can solve Inequalities.
4(5x + 2) ≤ 28

a)

x ≤ 1

b)

x ≥ 1

c)

x ≤ 8

d)

x ≥ 8

82.

solve 5( 6 + 3r) + 7 ≥ 127

a)

r ≤ 6

b)

r ≥ 6

c)

r ≤ -6

d)

r ≥ -6

83.

Solve:
3(y+5)≥21

a)

y≤2

b)

y≥2

c)

y≥12

d)

y≤12

84.

Solve:
-8(x - 3) - 4x < 108

a)

x > -38

b)

x > -14

c)

x > -7

d)

x < -38

85.

Solve. 5 - (x - 4) > -2

a)

x > 11

b)

x < 11

c)

x > -11

d)

x < -11

Solving Inequalities

Total questions: 85

Worksheet time: 6hrs 27mins

Similar Resources on Wayground