Free Printable Inequalities

1.

Solve the inequality.
x + 5 ≤ 13

a)

x ≥ 8

b)

x ≥ 18

c)

x ≤ 8

d)

x ≤ 18

2.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

3.

Pick the correct inequality.

a)

A

b)

B

c)

C

d)

D

4.

10 ≥ x - 3

a)

x ≤ 13

b)

x ≥ 13

c)

x ≤ 7

d)

x ≥ 7

5.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

6.

14 < -2a + 6 - 2a

a)

a > -2

b)

a < -2

c)

a > 2

d)

a < 2

7.

Which inequality matches the graph?

a)

A

b)

B

c)

C

d)

D

8.

When do you "flip the inequalities sign"?

a)

When you add or subtract a negative

b)

When it's a 1-step problem

c)

When you multiply or divide a negative

d)

When it's a 2-step problem

9.

-3x ≤ 18

a)

x ≤ -6

b)

x ≤ 6

c)

x ≥ 6

d)

x ≥ -6

10.

2x > 12

a)

x > 6

b)

x < 6

c)

x ≥ 6

d)

x ≤ 6

11.

Solve for x: 3x + 7 < 22

a)

x < -29/3

b)

x < -5

c)

x < 29/3

d)

x < 5

12.

Decide if the inequality is open circle or closed circle: 4x > 16

a)

Open Circle

b)

Closed Circle

c)

Flip the sign

d)

I don't know

13.

Do I flip the sign? -6x ≥ 36

a)

Open Circle

b)

Closed Circle

c)

Yes

d)

No

14.

Will the graph be an open circle or closed circle? -6x + 1 < 4

a)

Open Circle

b)

Flip the sign

c)

Closed Circle

d)

Don't flip the sign

15.

Solve for x: -2x - 3 ≤ 13

a)

x ≥ 8

b)

x ≥ -8

c)

x ≤ 8

d)

x ≤ -8

16.

Solve for x: 5x + 9 > 34

a)

x > -5

b)

x > 5

c)

x < -5

d)

x < 5

17.

x - 7 ≥ 4

a)

x ≥ 11

b)

x ≥ -11

c)

x ≥ 3

d)

x ≥ -3

18.

14 ≥ x - 8

a)

22 ≥ x

b)

-22 ≥ x

c)

6 ≥ x

d)

-6 ≥ x

19.

5x - 7 ≥ 8

a)

x ≥ 3

b)

x ≤ 3

c)

x = 3

d)

x ≠ 3

20.

9x - 3 > 6

a)

x > 1

b)

x < 1

c)

x ≥ 1

d)

x = 1

21.

Solve and graph.
p - 3 > -8

a)

A

b)

B

c)

C

d)

D

22.

What inequality does the number line graph represent?

a)

x ≥ 3

b)

x > 3

c)

x < -3

d)

x ≤ -3

23.

Solve and graph.
k - 13 > -51

a)

A

b)

B

c)

C

d)

D

24.

6 - 2h > 30

a)

h < 24

b)

18 > h

c)

h > 12

d)

h < -12

25.

7b - 3 < 11

a)

b < 2

b)

84 > b

c)

b > 2

d)

b < 84

26.

4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

27.

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

a)

≤, ≥

b)

<, >

28.

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

a)

<, >

b)

≤, ≥

29.

When graphing "AND" inequalites, shading looks like___

a)

Shading that always connects the 2 dots.

b)

Shading that always points away from each dot

c)

2 shaded arrows pointing in same direction(both left)

d)

2 shaded arrows pointing in same direction (both right)

30.

When graphing the solutions to "OR" inequalities, The shading looks like___

a)

Shading that connects the 2 dots

b)

Shading that points away and never crosses.

c)

Shading that points toward each other and ALWAYS crosses

d)

Shading that points opposite, but sometimes crosses.

31.

a)

x > -3 or x > 1

b)

x < -3 or x < 1

c)

x ≥ 3 and x ≤ 1

d)

x > -3 and x < 1

32.

a)

x ≤ 3 and x > -2

b)

x < -2 or x ≥ 3

c)

x > -2 or x < 3

d)

x < 3 and x ≥ -2

33.

a)

x < 0 or x ≥ 2

b)

x < 0 or x > 2

c)

x ≤ 0 or x ≥ 2

d)

x ≤ 0 or x > 2

34.

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

35.

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

36.

Solve:
3x + 2 < -4 or 4x + 4 > 24

a)

x < -2 or x > 5

b)

x < 2 or x > 5

c)

x < -2 and x > 5

d)

x < 2 and x > 5

37.

Solve:
3x + 2 < -7 or -4x + 5 < 1

a)

x < -3 and x < 1

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

38.

Solve: -3 ≤ 2x - 1 ≤ 5

a)

-1 ≤ x ≤ 3

b)

-2 ≤ x ≤ 6

c)

-3 ≤ x ≤ 3

d)

1 ≤ x ≤ 3

39.

Solve:
-4x + 1 ≤ 21 and 5x + 2 < 22

a)

x > -5 or x ≤ 4

b)

x ≥ -5 or x < 4

c)

x > -5 and x ≤ 4

d)

x ≥ -5 and x < 4

40.

Solve:
3x + 2 < -7 or -4x + 5 < 1

a)

x < -3 and x < 1

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

41.

Solve and graph:

a)

A

b)

B

c)

C

d)

D

42.

x+2<-4 or -5x<-15

a)

-6<x<3

b)

x<-3 and x>6

c)

x<-6 or x>3

d)

No Solution

43.

0 < x + 7 < 9

a)

-7<x and x<2

b)

-7<x or x<2

c)

-7>x and x>2

d)

-7>x or x>2

44.

Solve:

a)

A

b)

B

c)

C

d)

D

45.

1-4x≤2 or 5x≥25

a)

x≥ -5 or x≥5

b)

x≤ -4 and x≤ 8

c)

No Solutions

d)

None of the above

46.

What inequality is graphed?

a)

2 < x < 4

b)

2 ≤ x ≤ 4

c)

x > 2 or x < 4

d)

x ≥ 2 or x ≤ 4

47.

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

48.

What inequality is shown?
Pay close attention to the signs!

a)

x ≥ 0 OR x < 5

b)

0 ≤ x ≤ 5

c)

0 ≤ x < 5

d)

0 ≥ x > 5

49.

What inequality is shown?

a)

x ≥ -5 OR x < 4

b)

x ≤ -5 OR x > 4

c)

-5 ≤ x < 4

d)

-5 ≥ x > 4

50.

What inequality is shown?

a)

x ≥ 0 OR x < 5

b)

0 ≤ x ≤ 5

c)

0 ≤ x < 5

d)

0 ≥ x > 5

51.

Which compound inequality is graphed above?

a)

-2 ≤ x ≤ 2

b)

-2 ≥ x ≥ 2

c)

2 < x < -2

d)

-2 > x > 2

52.

Which compound inequality is graphed above?

a)

0 > x > 5

b)

0 < x > 5

c)

0 ≤ x ≥ 5

d)

0 ≥ x ≥ 5

53.

Which compound inequality is graphed above?

a)

-2 < x ≤ 2

b)

-2 > x ≤ 2

c)

-2 < x < 2

d)

-2 ≥ x < 2

54.

Which compound inequality is graphed above?

a)

-2 ≥ x > 5

b)

-2 < x > 5

c)

-2 ≤ x < 5

d)

-2 > x ≥ 5

55.

a)

A

b)

B

c)

C

d)

D

56.

Solve:

a)

A

b)

B

c)

C

d)

D

57.

−6 < 2t − 5 < 3

a)

−0.5 < t < 1

b)

0.5 < t < −1

c)

−11/2 < t < 2

d)

11/2 < t < −2

58.

Solve each compound inequality and graph its solution.

a)

A

b)

B

c)

C

d)

D

59.

When solving inequalities you must _________________ the inequality when ____________________ by a negative.

a)

flip; dividing

b)

ignore; multiplying and dividing

c)

flip; multiplying

d)

flip; multiplying and dividing

60.

Could x = 3 be solution to the inequality
6 < x + 5 ≤ 11?

a)

Yes

b)

No

61.

Could x = - 5 be a solution to the inequality -6 < 3x + 9 < 21?

a)

yes

b)

no

62.

Solve 24 > -3r > -9

a)

-8 < r < 3

b)

-8 > r > 3

c)

r > - 8 and r > 3

d)

r > -8 or r < 3

63.

Pick the correct letter for:
6 > x

a)

A

b)

B

c)

C

d)

D

64.

Solve:
$-3\ ≤\ 2x-1\ ≤\ 5$

a)

$-1\ ≤\ x\ ≤\ 3$

b)

$-2\ ≤\ x\ ≤\ 6$

c)

$-3\ ≤\ x\ ≤\ 3$

d)

$1\ ≤\ x\ ≤\ 3$

65.

Solve:
$-4x+1≤21\ and\ 5x+2<22$

a)

$x>-5\ \ or\ \ x≤4$

b)

$x≥-5\ \ or\ \ x<4$

c)

$x>-5\ \ and\ \ x≤4$

d)

$x≥-5\ \ and\ \ x<4$

66.

Solve:
$3x+2<-4\ or\ 4x+4>24$

a)

$x<-2\ or\ \ x>5$

b)

$x<2\ \ or\ \ x>5$

c)

$x<-2\ \ and\ \ x>5$

d)

$x<2\ \ and\ x>5$

67.

Simplify the following compound inequality:
$16\le2x+6<30$

a)

$x\ge5$ and $x<12$

b)

$x\ge2$ and $x<11$

c)

$x\ge5$ or $x<12$

d)

$x\ge2$ or $x<11$

Inequalities

Total questions: 67

Worksheet time: 6hrs 32mins

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