Master Linear Inequalities: Practice Quizzes for College Algebra

Question 1

Which inequality symbol means "less than or equal to"?

Accepted Answer

≤

Answer

<

Answer

>

Answer

≥

Question 2

Solve the inequality: 3/4a - 1/2 < 5/8

Accepted Answer

a > 1/3

Answer

a < 1/3

Answer

a > 3

Answer

a < 3

Question 3

Solve the compound inequality: 2x + 5 > 15 or x - 3 < 2

Accepted Answer

x > 5,  x < 5

Answer

x < 5,  x > 5

Answer

x > 5,  x > 5

Answer

x < 5,  x < 5

Question 4

Solve the inequality: 5x - 7 is less than 23. Show the solution on a number line.

Accepted Answer

x < 6, (-∞, 6)

Answer

x > 6, (6, ∞)

Answer

x ≥ 6, [6, ∞)

Answer

x ≤ 6, (-∞, 6]

Question 5

Solve the inequality and show your work: 3(x - 2) < 6

Accepted Answer

x < 4

Answer

x < 6

Answer

x < 2

Question 6

Which inequality notation represents "x is greater than or equal to 5"?

Accepted Answer

x ≥ 5

Answer

x ≤ 5

Answer

x > 5

Answer

x < 5

Question 7

Solve the inequality: 3x + 2 > 11

Accepted Answer

x > 3

Answer

x < 3

Answer

x > -3

Answer

x < -3

Question 8

Solve the inequality: 2(x - 1) ≥ 6

Accepted Answer

x ≥ 4

Answer

x ≤ 4

Answer

x ≥ 2

Answer

x ≤ 2

Question 9

Which of the following inequalities represents the solution set of the inequality x > 2 and x < 5?

Accepted Answer

2 < x < 5

Answer

2 ≤ x < 5

Answer

2 < x ≤ 5

Answer

2 ≤ x ≤ 5

Question 10

Translate the statement 'The sum of x and 5 is less than or equal to 10' into a mathematical inequality.

Accepted Answer

x + 5 ≤ 10

Answer

x + 5 < 10

Answer

5 + x ≤ 10

Answer

5 + x < 10

Question 11

Determine the solution set for the inequality -x + 2 < 5.

Accepted Answer

x > 3

Answer

x < 3

Answer

The inequality has no solution

Answer

The inequality is always true

Question 12

Translate the following statement into an algebraic inequality: The total of two numbers, x and y, is less than 10.

Accepted Answer

x + y < 10

Answer

x - y < 10

Answer

x * y < 10

Answer

x / y < 10

Question 13

Identify the inequality symbol that represents 'greater than or equal to'.

Accepted Answer

>=

Answer

>

Answer

<

Answer

<=

Question 14

Find the solution to the inequality 2x - 5 > 15 by isolating the variable x.

Accepted Answer

x > 10

Answer

x < 10

Answer

x = 10

Answer

x > 5

Question 15

Find the solution to the inequality 0.5x - 1.2 < 2.3 by isolating the variable x.

Accepted Answer

x < 7

Answer

x > 7

Answer

x = 7

Answer

x < 6

Question 16

Graph the inequality x - 2 < 0 on a number line by indicating the solution region.

Accepted Answer

An open circle at 2, extending left

Answer

An open circle at 2, extending right

Answer

A closed circle at 2, extending left

Answer

A closed circle at 2, extending right

Question 17

Which of the following inequalities has the solution set {x | x > -7}?

Accepted Answer

x - 7 ≥ 0

Answer

x + 7 < 0

Answer

-x + 7 ≤ 0

Answer

-x - 7 > 0

Question 18

Which of the following is the inequality that represents the statement: 'A number x is at least -2'?

Accepted Answer

x ≥ -2

Answer

x ≤ -2

Answer

x < -2

Answer

x > -2

Question 19

Which of the following is the inequality symbol representing 'greater than or equal to'?

Accepted Answer

≥

Answer

<

Answer

>

Answer

≤

Question 20

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x < 8

Answer

x > 3

Answer

x < 3

Question 21

Which inequality represents the statement: 'A number y is less than or equal to the sum of 5 and twice itself'?

Accepted Answer

y ≤ 5 + 2y

Answer

y ≥ 5 + 2y

Answer

y < 5 + 2y

Answer

y > 5 + 2y

Question 22

Solve the inequality: 3(x + 2) - 5 > 10

Accepted Answer

x > 5

Answer

x < 5

Answer

x > 3

Answer

x < 3

Question 23

Which of the following is equivalent to the inequality -2x + 5 > 11?

Accepted Answer

x > 3

Answer

x < 3

Answer

x > -3

Answer

x < -3

Question 24

Select the graph that depicts the solution region of the inequality y > 2x - 1

Accepted Answer

Shaded region above the line y = 2x - 1

Answer

Shaded region below the line y = 2x - 1

Answer

Shaded region to the right of the line y = 2x - 1

Answer

Shaded region to the left of the line y = 2x - 1

Question 25

Solve the inequality: |2x - 3| > 5

Accepted Answer

x < -1 or x > 4

Answer

x > -1 or x < 4

Answer

-4 < x < 1

Answer

x > 1 or x < -4

Question 26

Which inequality represents the condition "the sum of x and 5 is greater than 10"

Accepted Answer

x + 5 > 10

Answer

x + 5 < 10

Answer

x - 5 > 10

Answer

x - 5 < 10

Question 27

Solve the inequality: 3(x - 2) > 6

Accepted Answer

x > 4

Answer

x < 4

Answer

x > 2

Answer

x < 2

Question 28

Identify the number line that accurately represents the solution set of the inequality x - 1.5 < 2.5

Accepted Answer

(-----------------|--------------)-------->

Answer

(----------------|--------------)-------->

Answer

<----------(------------------|--------------)

Answer

<----------(-----------------|--------------)

Question 29

Translate the following condition into an inequality: "the difference between twice a number and 5 is less than or equal to 3"

Accepted Answer

2x - 5 ≤ 3

Answer

2x - 5 ≥ 3

Answer

2x + 5 ≤ 3

Answer

2x + 5 ≥ 3

Question 30

Solve the system of linear inequalities:  x + y ≤ 5 and x - y ≥ 1. Which of the following represents the solution set for x?

Accepted Answer

x ≤ 3 and x ≥ 2

Answer

x ≤ 2 and x ≥ 3

Answer

x < 3 and x > 2

Answer

x < 2 and x > 3

Question 31

What symbol represents 'not equal to'?

Accepted Answer

≠

Answer

=

Answer

<

Answer

>

Question 32

Solve the inequality: 2x - 5 > 9

Accepted Answer

x > 7

Answer

x < 7

Answer

x > -7

Answer

x < -7

Question 33

Which graph represents the inequality x ≤ 3?

Accepted Answer

A closed circle at 3 with a line extending leftward

Answer

An open circle at 3 with a line extending leftward

Answer

An open circle at 3 with a line extending rightward

Answer

A closed circle at 3 with a line extending rightward

Question 34

Which value is NOT a solution to the inequality 2x - 5 ≥ 1?

Accepted Answer

x = 1

Answer

x = 4

Answer

x = 3

Answer

x = 2

Question 35

What is the solution set for the inequality |x - 2| > 3?

Accepted Answer

x < -1 or x > 5

Answer

x < 1 or x > 5

Answer

-1 < x < 5

Answer

1 < x < 5

Question 36

You are working on a project and need to complete at least 13 tasks. You can complete 2 tasks per hour.  Which inequality represents the minimum number of hours (x) you need to work to finish the project?

Accepted Answer

2x ≥ 13

Answer

x + 2 ≥ 13

Answer

2x ≤ 13

Answer

x - 2 ≤ 13

Question 37

Which of the following inequalities is equivalent to 3x > 6?

Accepted Answer

x > 2

Answer

x < 6

Answer

x < 2

Answer

x > 6

Question 38

Translate the following statement into an inequality: 'A number decreased by 4 is greater than or equal to 5'.

Accepted Answer

x - 4 ≥ 5

Answer

5 - x ≤ 4

Answer

5 - x ≥ 4

Answer

x - 4 ≤ 5

Question 39

Which inequality represents the shaded area on the number line where -2 is included and 3 is excluded?

Accepted Answer

-2 ≤ x < 3

Answer

-2 > x ≥ 3

Answer

-2 ≥ x > 3

Answer

-2 < x ≤ 3

Question 40

Solve the absolute value inequality |x - 2| > 3. Which of the following represents the solution set?

Accepted Answer

x < -1 OR x > 5

Answer

-1 < x < 5

Answer

x > -1 AND x < 5

Answer

x < -1 AND x > 5

Question 41

Which of the following inequalities represents the statement 'x is greater than or equal to 3'?

Accepted Answer

x ≥ 3

Answer

x ≤ 3

Answer

x > 3

Answer

x < 3

Question 42

Which of the following inequalities is represented by the number line with a closed circle at 5 and shading to the right?

Accepted Answer

x ≥ 5

Answer

x < 5

Answer

x > 5

Question 43

A nurse needs to administer a medication that requires a patient's temperature to be below 100 degrees Fahrenheit. Which inequality represents this situation, where 't' represents the patient's temperature?

Accepted Answer

t < 100

Answer

t ≤ 100

Answer

t > 100

Question 44

A hospital has a maximum capacity of 200 patients. If 'p' represents the current number of patients, which inequality represents the situation where the hospital is not at full capacity?

Accepted Answer

p < 200

Answer

p ≥ 200

Answer

p ≤ 200

Answer

p > 200

Question 45

A doctor recommends that a patient consume at least 2 liters of water per day. If 'w' represents the daily water intake in liters, which inequality represents this recommendation?

Accepted Answer

w ≥ 2

Answer

w ≤ 2

Answer

w > 2

Answer

w < 2

Question 46

Which of the following is the solution to the inequality 2x - 5 > 11?

Accepted Answer

x > 8

Answer

x > 5

Answer

x < 8

Answer

x < 5

Question 47

Solve the inequality: -3(2x + 1) + 4 > 13

Accepted Answer

x < -2

Answer

x < 2

Answer

x > 2

Answer

x > -2

Question 48

Which inequality is represented by the number line below? [_________-]

Accepted Answer

x < 5

Answer

x ≤ 5

Answer

x ≥ 5

Answer

x > 5

Question 49

Solve the inequality: 1.5x - 2.5 > 4

Accepted Answer

x > 4.5

Answer

x < 4.5

Answer

x > 2.5

Answer

x < 2.5

Question 50

Which of the following is NOT a step in solving the inequality 2x - 3 ≤ 9?

Accepted Answer

Subtract 2 from both sides

Answer

Divide both sides by 2

Answer

Simplify both sides

Answer

Check the solution

Question 51

Solve the inequality: |x - 2| > 5

Accepted Answer

x < -3 or x > 7

Answer

x < 3 or x > 7

Answer

-3 < x < 7

Answer

3 < x < 7

Question 52

Which of the following inequalities is equivalent to 3x + 2 ≤ 11?

Accepted Answer

x ≤ 3

Answer

x ≥ 3

Answer

x ≥ -3

Answer

x ≤ -3

Question 53

Solve the compound inequality: -2 < 3x - 5 ≤ 10

Accepted Answer

-1 < x ≤ 5

Answer

-1 < x

Answer

x ≤ 5

Answer

x < 5

Question 54

Which of the following is true about the inequality x² - 9 ≥ 0?

Accepted Answer

The solution is x ≤ -3 or x ≥ 3

Answer

The solution is x ≤ 3

Answer

The solution is x ≥ -3

Answer

There is no solution

Question 55

Solve the inequality: (x - 2)² > 4

Accepted Answer

x < -2 or x > 6

Answer

x < 2 or x > 6

Answer

-2 < x < 6

Answer

2 < x < 6