# Worksheet: One-Variable Absolute Value Inequalities

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

**Q2: **

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.

- A189 g, 183 g
- B183 g, 6 g
- C183 g, 177 g
- D189 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

**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

**Q20: **

Express in the form of an absolute value inequality.

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- D

**Q21: **

Express the following as an absolute value inequality: , .

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- D

**Q22: **

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

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- 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.

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- B
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- D

**Q24: **

Express in the form of an absolute value inequality.

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- D

**Q25: **

Determine the absolute value inequality representing .

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- D