Free Printable Linear Inequality Review

1.

Which inequality is represented by the words " no more than" or "at most"?

a)

<

b)

>

c)

≤

d)

≥

2.

Which inequality is represented by the words " more than"?

a)

<

b)

>

c)

≤

d)

≥

3.

Which inequality is represented by the words "less than"?

a)

<

b)

>

c)

≤

d)

≥

4.

Which inequality is represented by the words " at least"?

a)

<

b)

>

c)

≤

d)

≥

5.

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile. Katie has no more than $10 to spend on the taxi ride.

a)

1.75 + 0.65m < 10

b)

1.75 + 0.65m > 10

c)

1.75m + 0.65 < 10

d)

1.75m + 0.65 > 10

6.

The dance committee hired a DJ for the fall dance. The DJ charges $125 per hour in addition to $55 for an assistant. The committee wants to keep the total cost under $600. Which inequality represents the maximum amount of hours the DJ will play at the dance?

a)

125x + 55 ≤ 600

b)

125x + 55 ≥ 600

c)

125x + 55 > 600

d)

125x + 55 < 600

7.

Write the linear inequality in standard form for this situation: Ms. Savva is ordering pizzas and breadsticks for a school party and has a budget of no more than $81. An order of breadsticks costs $7 and a pizza costs $13.

a)

7x + 13y < 81

b)

7x + 13y ≥ 81

c)

7x + 13y ≤ 81

d)

7x + 13y > 81

8.

Write the linear inequality in standard form for this situation: The manager of an electronics store projects that the store should achieve more than $21,000 in revenue from TVs and DVD players every day in order to remain profitable. Tvs sell for $225 and DVD players sell for $175.

a)

225x +175y ≤ 21,000

b)

225x +175y ≥ 21,000

c)

225x +175y < 21,000

d)

225x +175y > 21,000

9.

At the Big Bear video rental store, blank CDs cost $1.50 each and blank DVDs cost $3.25 each. Which of the following statements best describes the number of CDs (c) and DVDs (d) that can be purchased for less than $65.00?

a)

1.50c + 3.25d < 65.00

b)

3.25c + 1.50d <65.00

c)

1.50c + 3.25d ≤ 65.00

d)

3.25c + 1.50d ≤ 65.00

10.

Fuel x costs $2 per gallon and fuel y costs $3 per gallon. You have at most $18 to spend on fuel. Your tank can hold 14 gallons at most. Write a system to represent this situation.

a)

x+y≤14
2x+3y≤18

b)

2x+3y≤14
x+y≤18

c)

2x+y<18
x+3y<14

d)

x+14≤y
2x+3y≤18

11.

Sarah makes small purses (x) and big purses (y). She can make no more than 8 purses a week.

Which inequality represents the situation?

a)

x + y ≤ 8

b)

x + y > 8

c)

2x + 3y ≤ 6

d)

x + y ≤ 10

12.

It takes Sarah 2 hours to make small purses and 3 hours to make big purses. She has a maximum of 18 hours a week. Which inequality represents this situation?

a)

2x + 3y ≤ 18

b)

x + y ≤ 6

c)

x + y ≤ 9

d)

3x + 2y ≤ 18

13.

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined.

a)

35 nachos, 52 sodas

b)

18 nachos, 69 sodas

c)

52 nachos, 35 sodas

d)

61 nachos, 26 sodas

14.

Which of the following linear inequalities represents the graph?

a)

$y\ge3x-5$

b)

$y\ge\frac{1}{3}x-5$

c)

$y\le-\frac{1}{3}x-5$

d)

$y>\frac{1}{3}x+5$

15.

Which of the following linear inequalities represents the graph?

a)

$x\ge2$

b)

$x\ge-2$

c)

$y\ge-2$

d)

$y>-2$

16.

When graphing a linear inequality, $\le$ and $\ge$ signs would require you to draw...

a)

a solid line

b)

a dotted line

17.

Which point below is NOT part of the solution set?

a)

(0, 0)

b)

(-10, -10)

c)

(-1, 5)

d)

(5, 20)

18.

Which of the following is a solution to the systems of inequalities?

a)

(0, 0)

b)

(-3, 0)

c)

(2, -5)

d)

(3, -1)

19.

Which of the following is NOT a solution to the systems of inequalities?

a)

(0, 0)

b)

(3, -2)

c)

(3, -4)

d)

(4, -4)

20.

Which system of inequalities is shown?

a)

y ≥ -x - 1
y < x + 4

b)

y < -x - 1
y ≥ x + 4

c)

y > -x - 1
y ≥ x + 4

d)

y > -x - 1
y ≥ x + 3

21.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

22.

Which point is a solution?

a)

(0, 6)

b)

(-3, 4)

c)

(1, 0)

d)

(-4, 3)

23.

Which ordered pair is a solution of the inequality?

y ≥ 4x – 5

a)

(3, 4)

b)

(3, 0)

c)

(2, 1)

d)

(1, 1)

24.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

25.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

_D

26.

Select the correct graph for each inequality.

a)

A

b)

B

c)

C

d)

D

27.

Which of the following is not a solution to this system of inequalities?

a)

(0,-1)

b)

(0,3)

c)

(4,0)

d)

(6,-2)

28.

Your family goes to a southern style restaurant for dinner. There are 6 total people in your family. Some order chicken for $14 and the rest order steak for $17. The total bill is $99. Write a system that could represent this situation.

a)

c + s = 6
14c + 17s = 99

b)

c + s = 99
14c + 17s = 6

c)

c + s = 6
17c + 14s = 99

d)

c + s = 99
17c + 14s = 6

29.

a)

A

b)

B

c)

C

d)

D

30.

Which region in the graph shown represents the solution to the following system of linear inequalities?
2x - y > 6
3y ≤ x - 6

a)

Region A

b)

Region B

c)

Region C

d)

Region D

31.

Which region represents the solution to the following system of inequalities?
y ≤ x + 2
y ≤ -x+ + 4

a)

Region F

b)

Region G

c)

Region H

d)

Region J

32.

Determine if (0, 1) is a solution to $y>-6x+1$ .

a)

(0,1) is a solution

b)

(0, 1) is not a solution.

33.

For a party, you can spend no more than $12 on peanuts and

cashews. Peanuts are $2.00/lb. and cashews are twice that. Which graph represents the solution set for this situation?

a)

b)

c)

d)

34.

When graphing an inequality, which symbols tell you to use a dashed line?

a)

<, >

b)

≤, ≥

35.

Does the sign need to flip when solving?
-2x ≥ 22

a)

YES

b)

NO

36.

Will my line be solid?
5 ≥ x

a)

Yes

b)

No

37.

When graphing a linear inequality, $\le$ and $\ge$ signs would require you to draw...

a)

a solid line

b)

a dotted line

38.

When graphing a linear inequality, < and > signs would require you to draw...

a)

a solid line

b)

a dotted line

39.

Which of the following linear inequalities represents the graph?

a)

$x\ge2$

b)

$x\ge-2$

c)

$y\ge-2$

d)

$y>-2$

40.

Which of the following linear inequalities represents the graph?

a)

$y\ge3$

b)

$x\ge3$

c)

$y\le3$

d)

$y<3$

41.

Solve the system of inequalities by graphing.

a)

b)

c)

d)

42.

Solve the system of inequalities by graphing. $8x\ +4y\ge10\ and\ 3x-6y>12$

a)

b)

c)

d)

43.

Identify the graph represented by the following system of inequalities.

2x - y > 4

4x + 2y < 6

a)

b)

c)

44.

Colin needs to save at least $200 for homecoming. He works 2 jobs earning $9/hour at Wawa and $25/hour mowing lawns. He only has time to work 16 hours before homecoming.

a)

x + y ≥ 25

x + y ≤ 9

b)

100x + 25 y ≤ 200

2x + 9y ≤ 16

c)

x + y ≥ 200

9x + 25y ≤ 16

d)

9x + 25y ≥ 200

x + y ≤ 16

45.

Which system of inequalities represents the graph. (Click on image to view graph)

a)

4x+3y>9

x-3y<6

b)

$4x-3y<9$
$x+3y>6$

c)

$4x-3y<9$
$x+3y<6$

d)

$4x+3y<9$
$x-3y>6$

46.

In a system of inequality, the shaded area of where the two graphs overlap mean the points are solutions of all the inequalities in the system.

a)

True

b)

False

47.

Another solution to the graph of the example is? (Click on the graph to enlarge image)

a)

2,1

b)

-4,2

c)

4,2

d)

-2,1

48.

Write an inequality represented by the graph.

a)

x < - 3

b)

y < - 3

c)

x > - 3

d)

x ≥ - 3

49.

Are the points on the boundary line part of the solution set or not?

a)

Yes, they are part of the solution set

b)

No, they are NOT part of the solution set

50.

Which system of inequalities matches the graph?

a)

y < x−2

y < 3

b)

y > -x+2

y > 3

c)

y < -x+2

y < 3

d)

y < -x+2

y > 3

51.

This system of inequalities has an infinite number of solutions, TRUE or FALSE?

a)

TRUE

b)

FALSE

Linear Inequality Review

Total questions: 51

Worksheet time: 13hrs 45mins

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