Free Printable Inequalities

1.

What inequality does the number line graph represent?

a)

x > 5

b)

x < −5

c)

x ≥ 5

d)

x ≥ −5

2.

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

a)

≤, ≥

b)

<, >

c)

≤, <

d)

≥, >

3.

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

a)

<, >

b)

≤, ≥

c)

≤, <

d)

≥, >

4.

What inequality does the number line graph represent?

a)

x ≤ -4

b)

x ≥ -4

c)

x < -4

d)

x < 4

5.

Would you use a closed or open circle to graph x < 3?

a)

Closed

b)

Open

6.

Which graph matches the inequality
r ≥ -6?

a)

A

b)

B

c)

C

d)

D

7.

Which graph matches the inequality

k < 3?

a)

A

b)

B

c)

C

d)

D

8.

What inequality does the number line graph represent

a)

x ≤ 4

b)

x ≥ -4

c)

x < -4

d)

x < 4

9.

Level 1

When do we switch the inequality symbol?

a)

when multiplying or dividing by a NEGATIVE

b)

when adding and subtracting a NEGATIVE

c)

we never switch the inequality

d)

When there is a negative in the problem

10.

Write an expression.
Anita needs at least an 90 grade (g) on her test to get an A in math class.

a)

g ≤ 90

b)

g ≥ 90

c)

g < 90

d)

g > 90

11.

126 < f + 32

a)

f > 94

b)

f < 96

c)

f < 94

d)

f < 55

12.

Solve the inequality

a)

$y<66$

b)

$y>66$

c)

$y>6$

d)

$y<6$

13.

Solve the inequality

a)

$x>11$

b)

$x>-11$

c)

$x<11$

d)

$x<-11$

14.

Kate is saving to take an SAT prep

course that costs $350. So far, she has

saved $180, and she adds $17 to her

savings each week. Which equation represents this situation?

a)

350 + 17w = 180

b)

17 + 180w = 350

c)

17w + 180 = 350

d)

17w - 180 = 350

15.

Level 1

Write an inequality for the statement:

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

16.

Level 2

-4 + y < -8

a)

y < 4

b)

y < -12

c)

y < -4

d)

y < 12

17.

Level 2

Solve.

a)

z≤1

b)

z>9

c)

z≤9

d)

z<9

18.

Level 2

The room can hold a maximum of 400 people. If there are already 134 people there, how many more can come? Identify the inequality that represents this situation.

a)

x - 134 < 400

b)

x + 134 < 400

c)

x - 134 ≤ 400

d)

x + 134 ≤ 400

19.

Level 3

What are two solutions to x < 8?

a)

8.6, 7.9

b)

11, 16

c)

0.8, 5.9

d)

12, 7.1

20.

Each gumball in a gumball machine costs $0.25. You can spend no more than $2.50 in total on gumballs.

Which inequality would represent how many gumballs you could buy?

a)

$0.25x\ <\ 2.50$

b)

$0.25x\ >\ 2.50$

c)

$0.25x\ \le\ 2.50$

d)

$0.25x\ \ge\ 2.50$

21.

Level 3

Solve the inequality.

a)

x ≤ 6

b)

x ≥ 6

c)

x ≤ -6

d)

x ≥ -6

22.

What is the name of this symbol:

<

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

23.

What is the name of this symbol:

>

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

24.

What is the name of this symbol:

\le

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

25.

What is the name of this symbol:

\ge

a)

less than

b)

greater than

c)

less than or equal to

d)

greater than or equal to

26.

Solve: -2x ≤ 14

a)

x ≤ 7

b)

x ≤ -7

c)

x ≥ 7

d)

x ≥ -7

27.

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

28.

Do I need to flip my sign?
-3x ≥ 12

a)

Yes

b)

No

29.

Do I need to flip my sign?

-3 + x ≥ -12

a)

Yes

b)

No

30.

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

(a)

31.

The hole for a birdfeeder post is 3 feet deep. The top of the post needs to be at least 5 feet above the ground.

Which of the following inequalities would correctly represent the required length of the post?

a)

x\ \ge\ 5

b)

$x\ \le\ 5$

c)

$x\ -\ 3\ \ge\ 5$

d)

$x\ +\ 3\le\ 5$

32.

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

What is the key word or words that would tell you what inequality symbol to use to solve this problem?

(a)

33.

Solve:

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

a)

All real numbers

b)

x < -3 and x > 1

c)

x < -3 or x < 1

d)

x < -3 or x > 1

34.

You can spend no more than $35 on a shopping trip. You want to buy a shirt that costs $14. If you buy the shirt, how much money would you have left?

Which inequality would help you solve this problem correctly?

a)

$x\ +\ 14\ \le\ 35$

b)

$x\ +\ 14\ \ge35$

c)

$x\ -\ 14\ \ge35$

d)

$x\ -\ 14\ \le\ 35$

35.

You have $30 to buy baseball cards. Each pack of cards costs $5. Write an inequality that represents the number of packs of baseball cards you can buy and still have at least $10 left.

a)

$30\ -\ 5x\ \ge10$

b)

$30\ -\ 5x\ \le\ 10$

c)

$30\ -\ 5x\ <\ 10$

d)

$30\ -\ 5x\ >\ 10$

36.

You borrow $200 from a friend to help pay for a new laptop computer. You pay your friend back $12 per week. Write and solve an inequality to find when you will owe your friend less than $56.

Which one of the following inequalities would be the correct answer?

a)

x < 12

b)

x > 12

c)

x < 21

d)

x > 21

37.

Kate needed $100 to buy a graphing calculator for her math class. Her neighbor will pay her $5 per hour to babysit and her Father gave her $10 for mowing the lawn. Which inequality represents the minimum amount of hours she will need to babysit in order for her to buy her calculator?

a)

5x + 10 ≥ 100

b)

5x - 100 ≥ 10

c)

10x + 5 ≤ 100

d)

5x + 10 > 100

38.

6(n + 2) < -72

a)

n < -14

b)

n < 35/3

c)

n < -10

d)

n > -14

39.

6x + 10 > 5x - 12

a)

x > 2

b)

x < -2

c)

x < -22

d)

x > -22

40.

Solve the following "and" Compound Inequality

$-27<7x-13<8$

a)

$x>-2\ and\ x<3$

b)

$x<-2\ and\ x<3$

c)

$x>-2\ and\ x>3$

d)

$x>2\ and\ x<3$

41.

4(2a + 3) < 3(a - 1)

a)

a < -3

b)

a > -3

c)

a < 3

d)

a > 3

42.

Solve:
6x+10>5x-12

a)

x>2

b)

x<2

c)

x<-22

d)

x>-22

43.

a)

a ≥ 4

b)

a ≥ -4

c)

a ≤ -4

d)

No solution

44.

What inequality is graphed?

a)

2 < x ≤ -3

b)

2 < x < -3

c)

x > 2 or x ≤ -3

d)

x > 2 or x < -3

45.

Select the correct inequality for the graph.

a)

-1 ≤ x < 6

b)

1 ≤ x < 6

c)

1 < x ≤ 6

d)

x ≤ 1 or x > 6

46.

-2 < x - 9 < 3

a)

x < 12

b)

7 < x

c)

7 < x < 12

d)

x > 7 or x < 12

47.

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

48.

Every day, a man needs to eat more than 1800 but less than 1900 calories. Write an inequality representing the possible amount of calories you could get.

a)

1800 ≤ c ≤ 1900

b)

1800 ≤ c < 1900

c)

1800 < c ≤ 1900

d)

1800 < c < 1900

49.

−6 < 2t − 5 < 3

a)

−0.5 < t < 1

b)

0.5 < t < −1

c)

−11/2 < t < 2

d)

11/2 < t < −2

50.

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

51.

$-20<-10+x\le0$

a)

$x\le10$

b)

$-10<x\le10$

c)

$x>-10$

d)

$All\ Solutions$

52.

Which graph represents

-5\ ≤\ x\ ≤\ 5

?

a)

Graph 1

b)

Graph 2

c)

Graph 3

d)

Graph 4

53.

Which of the following is a compound inequality with "or"

a)

b)

c)

54.

What inequality is being represented?

a)

$5\ <\ x\ <\ 9$

b)

$5\ ≤\ x\ ≤\ 9$

c)

$5\ <\ x\ ≤\ 9$

d)

$5\ ≤\ x\ <\ 9$

55.

When graphing "AND" inequalites, shading looks like___

a)

Shading that always connects the 2 circles.

b)

Shading that always points away from each circle.

c)

2 shaded arrows pointing in same direction (both left).

d)

2 shaded arrows pointing in same direction (both right).

56.

Find the solution for:

-4x + 1 ≤ 21 and 5x + 2 < 22

a)

not possible

b)

x ≥ -5 or x < 4

c)

x > 22/4 and x < 24/5

d)

x ≥ -5 and x < 4

57.

Does the following graph match the compound inequality

$x<1\ or\ x\ge3$

a)

True

b)

False

58.

Solve the following Compound Inequality $2x+9>17\ or\ 5x+10<10$

a)

$x<0\ or\ x<4$

b)

$x>0\ or\ x>4$

c)

$x<0\ or\ x>4$

d)

$x>0\ or\ x<4$

59.

Which graph matches the following "And" Compound Inequality

$x>-2\ and\ x<3$

a)

b)

60.

Solve the following Compound Inequality $-3\left(2x+1\right)<-15\ or\ 1-x\ge5$

a)

$x\ge2\ or\ x\le-4$

b)

$x\le-4\ or\ x>2$

c)

$x\ge-4\ or\ x<2$

d)

$x<-4\ or\ x>2$

Inequalities

Total questions: 60

Worksheet time: 5hrs 26mins

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