Free Printable Solving and Graphing Inequalities

Free Printable Worksheets

Worksheets

Solving and Graphing Inequalities

Total questions: 59

Worksheet time: 3hrs 44mins

Name

Class

Date

1.

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

a)

≤, ≥

b)

<, >

2.

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

a)

<, >

b)

≤, ≥

3.

10 ≥ x - 3

a)

x ≤ 13

b)

x ≥ 13

c)

x ≤ 7

d)

x ≥ 7

4.

8x ≥ -32

a)

x ≥ -4

b)

x ≥ 4

c)

x ≤ -4

d)

x ≥ 4

5.

4x - 2 ≤ -22

a)

x ≥ -5

b)

x ≥ -6

c)

x ≤ -6

d)

x ≤ -5

6.

s + 9 ≥ -25

a)

s ≥ -18

b)

s ≥ -34

c)

s ≤ 18

d)

s ≥ 34

7.

6 - 2h > 30

a)

h < 24

b)

18 > h

c)

h > 12

d)

h < -12

8.

-7 + 10z > -27

a)

z < -2

b)

z > -34

c)

2 > z

d)

z > -2

9.

-4x + 14 ≤ 54

a)

x ≥ -10

b)

x ≤ -10

c)

x ≥ 10

d)

x ≤ 10

10.

Match the graph with its inequality.

a)

a > 11

b)

a < 11

c)

a ≤ 11

d)

a ≥ 11

11.

3y + 15 > 0

a)

y > -5

b)

y < -5

c)

y > 5

d)

y < 5

12.

2x - 4 ≤ 16

a)

x ≤ 6

b)

x ≥ 6

c)

x ≤ 10

d)

x ≥ 10

13.

Write an Inequality Statement for the statement.

14.

Write an Inequality Statement for the statement.

15.

Write an Inequality Statement for the statement.

"In order to drive you must be at least 16 years old."

16.

Write an Inequality Statement for the statement.

17.

Write an Inequality Statement for the statement.

18.

Write an Inequality Statement for the statement.

19.

Solve the one step Inequality.

20.

Solve the Two - step Inequality.

21.

Solve the Two - step Inequality.

22.

When solving an inequality, how is the solution impacted when you divide by a negative number?

a)

When you divide by a negative, you must flip the sign.

b)

Nothing happens, you solve it like normal.

c)

You only flip the sign if the answer is negative.

23.

What happens to the inequality sign when you multiply both sides by a negative number?

a)

The inequality sign remains the same.

b)

The inequality sign flips direction.

c)

The inequality sign becomes an equal sign.

24.

Which inequality represents the solution to the equation 5x + 3 ≤ 18?

a)

x ≥ 3

b)

x ≤ 3

c)

x ≤ 5

d)

x ≥ 5

25.

When graphing the inequality x > 4, what type of dot is used on the number line?

a)

Open dot

b)

Closed dot

26.

When graphing the inequality y ≤ -3, what type of dot is used on the number line?

a)

Open dot

b)

Closed dot

27.

When graphing the inequality x ≤ -2, what type of dot is used on the number line?

a)

Closed dot

b)

Open dot

28.

Select the Symbol that represents the following keywords:

Fewer than, smaller than, below, under

A

B

C

D

29.

Select the Symbol that represents the following keywords:

more than, bigger than, above, over

A

B

C

D

30.

Select the Symbol that represents the following keywords:

maximum, no more than, at most

A

B

C

D

31.

Select the Symbol that represents the following keywords:

minimum, at least, no less than

A

B

C

D

32.

Which inequality matches the graph?

a)

x<3

b)

x>3

c)

x<3

d)

x>3

33.

Which inequality matches the graph?

a)

x>-2

b)

x<-2

c)

x>-2

d)

x<-2

34.

You can spend no more than 20 dollars on your mom's birthday present.

a)

x > 20

b)

x < 20

c)

x ≤ 20

d)

x ≥ 20

35.

The band practice will be less than 45 minutes long on Friday. Which inequality represents this situation?

a)

p < 45

b)

p > 45

c)

p ≤ 45

d)

p ≥ 45

36.

There are fewer than 150 children at the playground.

a)

c<150

b)

c>150

c)

c≤150

d)

c≥150

37.

All items at Pat's Pasta cost more than $10. Which inequality represents this situation?

a)

i < 10

b)

i > 10

c)

i ≤ 10

d)

i ≥ 10

38.

My sister plans to sell more than 250 boxes of cookies.

a)

c>250

b)

c<250

c)

c≤250

d)

c≥250

39.

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

40.

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

41.

The keywords "minimum" are used with which symbol?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

42.

The keywords "no more than" are used with which symbol?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

43.

The keywords "no less than" are used with which symbol?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

44.

$x>-2$

a)

b)

c)

d)

45.

$x<-2$

a)

b)

c)

d)

46.

The keywords "no less than" are used with which symbol?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

47.

-3x - 5 $\ge$ 10

x

\le

?

(a)

48.

-3x + 1 $\ge$ -8

x

\le

?

(a)

49.

-2x - 3 $\ge$ 7

x $\le$ ?

(a)

50.

-x $\le$ -4

x

\ge

?

(a)

51.

-2x $\le$ 4

x

\ge

?

(a)

52.

Which symbol says "less than"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

53.

Which symbol says "greater than"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

54.

Which symbol says "less than or equal to"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

55.

Which symbol says "greater than or equal to"?

a)

$<$

b)

$>$

c)

$\le$

d)

$\ge$

56.

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

57.

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

58.

Which inequality matches the graph?

a)

x<3

b)

x>3

c)

x<3

d)

x>3

59.

Match the graph with its inequality.

a)

11 < a

b)

11 > a

c)

11 ≤ a

d)

11 ≥ a

100 %

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