Free Printable Inequalities and 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.

A student must be at least 15 years old to obtain a driver’s permit.

a)

x > 15

b)

x < 15

c)

x ≤ 15

d)

x ≥ 15

3.

To order from the kids menu a person must be no more than 12 years old.

a)

x > 12

b)

x < 12

c)

x ≥ 12

d)

x ≤ 12

4.

You bike for 2 hours at a speed no faster than 17.6 miles per hour. Write and solve an inequality that represents the possible numbers of miles you bike.

a)

X ≤ 17.6

b)

X ≥ 17.6

c)

X ≥ 35.2

d)

X ≤ 35.2

5.

Which of the following inequalities would require you to flip the sign when solving?

a)

2x < 3

b)

3x > - 9

c)

-4x ≥ 10

d)

5x ≤ 15

6.

Solve:
-4(-7-5x) > 188

a)

x < -32

b)

x > -32

c)

x < 8

d)

x > 8

7.

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

a)

x ≥ -10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

8.

Mike is 6 years younger than twice Iris's age. What expression can be used to find Mike’s age?

a)

6 + 2a

b)

6 - 2a

c)

2a - 6

d)

12 - a

9.

Melissa wants to spend no more than $300 on school clothes. She spends $75 on a coat and then wants to buy some sweaters that are on special for $10 each. Write an inequality to show how many sweaters Melissa can buy. DO NOT SOLVE

a)

75x-10 ≥ 300

b)

75+10 ≤ 300x

c)

10x ≥ 300

d)

75+10x ≤ 300

10.

Match the graph with the given solution.

a)

A

b)

B

c)

C

d)

D

11.

Solve and then match the correct solution & graph.

a)

A

b)

B

c)

C

d)

D

12.

A beekeeper charges $3.00 for each jar of honey she sells at the farmers market. If she needs to make at least $43, how many jars does she need to sell?

a)

14.33 jars

b)

14 jars

c)

15 jars

d)

16 jars

13.

The keywords "at most" are used with which of the following symbols?

a)

≤

b)

>

c)

<

d)

≥

14.

The keywords "at least" are used with which of the following symbols?

a)

≥

b)

≤

c)

>

d)

<

15.

x - 7 ≥ 4

a)

x ≥ 11

b)

x ≥ -11

c)

x ≥ 3

d)

x ≥ -3

16.

14 ≥ x - 8

a)

22 ≥ x

b)

-22 ≥ x

c)

6 ≥ x

d)

-6 ≥ x

17.

Which of the following symbols means "less than"?

a)

<

b)

>

c)

≤

d)

≥

18.

Which of the following symbols means "more than"?

a)

>

b)

<

c)

≤

d)

≥

19.

Which of the following symbols means "less than or equal to"?

a)

≤

b)

<

c)

>

d)

≥

20.

Which of the following symbols means "greater than or equal to"?

a)

≥

b)

≤

c)

>

d)

<

21.

5x - 7 ≥ 8

a)

x ≥ 3

b)

x ≤ 3

c)

x = 3

d)

x ≠ 3

22.

9x - 3 > 6

a)

x > 1

b)

x < 1

c)

x ≥ 1

d)

x = 1

23.

The keywords "not equal to" are used with which of the following symbols?

a)

≠

b)

≤

c)

>

d)

<

24.

Solve and graph.
p - 3 > -8

a)

A

b)

B

c)

C

d)

D

25.

Solve and graph.
k - 13 > -51

a)

A

b)

B

c)

C

d)

D

26.

What inequality does the number line graph represent?

a)

x ≥ 3

b)

x > 3

c)

x < -3

d)

x ≤ -3

27.

Solve. 4x - 4 > 8

a)

x > 6

b)

x > 48

c)

x > 1

d)

x > 3

28.

Solve. 3x + 2 > 14

a)

x > 4

b)

x > 36

c)

x > 5 1/3

d)

x > 48

29.

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

a)

≤, ≥

b)

<, >

30.

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

a)

<, >

b)

≤, ≥

31.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

32.

Fewer Than

a)

<

b)

>

c)

≤

d)

≥

33.

No More Than

a)

<

b)

>

c)

≤

d)

≥

34.

more than

a)

<

b)

>

c)

≤

d)

≥

35.

At Least

a)

<

b)

>

c)

≤

d)

≥

36.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

37.

What inequality does the number line graph represent?

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

38.

Do I need to flip my sign?
3x ≥ 12

a)

Yes

b)

No

39.

Solve and graph.
k - 13 > -51

a)

A

b)

B

c)

C

d)

D

40.

-4x + 14 ≤ 54

a)

x ≥ - 10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

41.

10 < 3x + 19

a)

x < 3

b)

x > 3

c)

x < -3

d)

x > -3

42.

what does the number line show

a)

x = 3

b)

x > 3

c)

x < 3

d)

x > 6

43.

What is the inequality for:

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

44.

$5x-10=0$

a)

x = 5

b)

x = -5

c)

x = 2

d)

x = -2

45.

$2x+10=22$

a)

x = 12

b)

x = 24

c)

x = 16

d)

x = 6

46.

$\frac{x}{5}-2=8$

a)

x = 2

b)

x = 50

c)

x = 30

d)

x = 4

47.

$\frac{x\ +\ 1}{4}=12$

a)

x = 2

b)

x = 4

c)

x = 49

d)

x = 47

48.

$\frac{x\ -\ 7}{2}=14$

a)

x = 35

b)

x = 21

c)

x = 14

d)

x = 0

49.

$3x\ -\ 9\ =\ -18$

a)

x = 3

b)

x = -3

c)

x = 9

d)

x = -9

50.

$x\ +\ 5\ =\ 11$

a)

x = 16

b)

x = 6

c)

x = 55

d)

x = 11/5

51.

$x\ -\ 11\ =\ 22$

a)

x = 33

b)

x = 11

c)

x = 242

d)

x = 2

52.

7x = 21

a)

x = 28

b)

x = 14

c)

x = 147

d)

x = 3

53.

$-2x\ -\ 6\ =\ 14$

a)

x = 10

b)

x = -10

c)

x = 4

d)

x = -4

54.

BONUS: $9\ -\ 2x\ =\ -27$

a)

x = -9

b)

x = 9

c)

x = -18

d)

x = 18

55.

x - 8 = -5

a)

13

b)

-13

c)

3

d)

-3

56.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

57.

Solve the equation:
-5x = 25

a)

x = 20

b)

x = -20

c)

x = -5

d)

x = 5

58.

Solve the equation.

a)

24

b)

¹⁴⁷/₈ or 18³/₈

c)

168

d)

-24

59.

Solve the equation.

a)

-90

b)

90

c)

-40

d)

-180

60.

Which equation has x=9 as a solution

a)

4 + x = 12

b)

5x = 45

c)

2x = 20

d)

x + 7 = 26

61.

x + 12 = -20

a)

x = 32

b)

x = -32

c)

x = 8

d)

x = -8

62.

^a⁄₃+ 7= 13

a)

a= 2

b)

a= 6

c)

a= 18

d)

a= 20

63.

a)

1

b)

-1

c)

37

d)

-13

64.

a)

-12

b)

-4

c)

4

d)

12

65.

a)

4

b)

-4

c)

-12

d)

12

66.

a)

-4

b)

4

c)

24

d)

-24

67.

a)

-13

b)

13

c)

3

d)

-3

68.

a)

21

b)

14

c)

-14

d)

-21

69.

a)

-10

b)

10

c)

50

d)

-50

70.

a)

90

b)

19

c)

-19

d)

-90

71.

a)

0

b)

-0

c)

20

d)

-20

72.

²/₃ x - 4 = -10

a)

21

b)

-4

c)

9

d)

-9

73.

19 + a = -50

a)

a = -950

b)

a = -69

c)

a = -31

d)

a = -50/19

74.

x - 8 = -5

a)

13

b)

-13

c)

3

d)

-3

75.

3c + 5 = 23

a)

c = 3

b)

c = 6

c)

c = 7

d)

c = 18

76.

15 = 2a + 7

a)

2

b)

4

c)

12

d)

14

77.

What is the first step to solve this equation:
11 - 3x = 44

a)

Add 3 to both sides

b)

Subtract 11 from both sides

c)

Add 11 to both sides

d)

Divide 3 on both sides.

78.

x - 62 = 123
How should you show your work to isolate the variable and solve the equation?

a)

Add 62 to each side.

b)

Subtract 62 from each side.

c)

Multiply each side by 62.

d)

Add 123 to each side.

79.

Figure out what n equals in this equation:
6n + 4 = -26

a)

n=-6

b)

n= -5

c)

n= 8

d)

n= -4

80.

Translate the statement into an equation:

Five less than a number is 6

a)

n - 5 = 6

b)

5 - n = 6

c)

6 - 5 = 1

81.

What is the solution of 6d = 24

a)

d = 4

b)

d = 5

c)

d = 18

d)

d = 144

82.

Which equation has x=9 as a solution

a)

4 + x = 12

b)

5x = 45

c)

2x = 20

d)

x + 7 = 26

83.

x + 12 = -20

a)

x = 32

b)

x = -32

c)

x = 8

d)

x = -8

84.

u/4=12

a)

u = 3

b)

u = 8

c)

u = 16

d)

u = 48

85.

Solve:

-4x = 24

a)

x = 6

b)

x = -6

c)

x = 20

d)

x = 28

86.

Translate the sentence into an equation:

The product of a number and two-thirds is 24.

a)

2/3 + x = 24

b)

2/3 x = 24

c)

3/2 x = 24

d)

x + 2/3 = 24

87.

Translate the statement into an equation:
6 less than twice a number is 4

a)

2n - 6 = 4

b)

6 - 2n = 4

88.

Two more than 4 times a number is -18.

a)

4x + 2 = -18

b)

2x + 4 = -18

c)

18 = 4x + 2

89.

-4y = 48

a)

x = -52

b)

x = -12

c)

x = -44

d)

x = -13

90.

x + 12 = 20

a)

x = 32

b)

x = -32

c)

x = 8

d)

x = -8

Inequalities and inequalities

Total questions: 90

Worksheet time: 3hrs 0mins

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