# Worksheet: One-Variable Absolute Value Inequalities

In this worksheet, we will practice solving inequalities that contain absolute values.

Q1:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q2:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q3:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q4:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q5:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q6:

A factory produces cans with weight grams. To control the production quality, the cans are only allowed to be sold if . Determine the heaviest and the lightest weight of a can that can be sold.

• A 189 g, 183 g
• B 183 g, 6 g
• C 183 g, 177 g
• D 189 g, 177 g

Q7:

Which of the following represents the interpretation for ?

• AThe distance between 5 and is greater than .
• BThe distance between and is greater than 5.
• CThe distance between and is greater than 5.
• DThe distance between and is less than 5.
• EThe distance between and is less than 5.

Q8:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q9:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q10:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q11:

Suppose that and . Which of the following is true?

• A
• B
• C
• D
• E

Q12:

Suppose . If , which of the following statements is true?

• A
• B
• C
• D
• E

Q13:

Solve .

• A
• B
• C
• D

Q14:

Solve .

• A
• Bno solution
• C
• D
• Eany number

Q15:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q16:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q17:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q18:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q19:

Use the absolute value to write an inequality statement which describes all values that are a distance of 8 from the number 3.

• A
• B
• C
• D

Q20:

Express in the form of an absolute value inequality.

• A
• B
• C
• D

Q21:

Express the following as an absolute value inequality: , .

• A
• B
• C
• D

Q22:

Given that students’ marks in an exam range from 69 to 93, write an absolute value inequality to express the range of marks.

• A
• B
• C
• D

Q23:

An algae in the ocean can reach a maximum depth of 138 meters. Let represent the depth of an algae. Express, in the form of an absolute value, the range of values that can take.

• A
• B
• C
• D

Q24:

Express in the form of an absolute value inequality.

• A
• B
• C
• D

Q25:

Determine the absolute value inequality representing .

• A
• B
• C
• D