# Worksheet: 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

**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: **

A body was moving with a uniform velocity of magnitude 5 cm/s from the point to the point passing through the point without stopping. The distance between the body and the point is given by , where is the time in seconds, and is the distance in cm. Determine the distance between the body and the point after 5 seconds and after 11 seconds.

- A 5 cm, 5 cm
- B 15 cm, 5 cm
- C 3 cm, 40 cm
- D 15 cm, 15 cm

**Q6: **

A body moved from position to position passing through position with a uniform velocity of 3 cm/s and without stopping. If the distance between the body and position is given by , where is the time in seconds, and is the distance in centimetres, determine the time interval during which the body is less than 9 cm from .

- A
- B
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- D

**Q7: **

Find algebraically the solution set of the inequality .

- A
- B
- C
- D

**Q8: **

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 183 g, 177 g
- B 189 g, 183 g
- C 183 g, 6 g
- D 189 g, 177 g

**Q9: **

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 less than 5.
- DThe distance between and is greater than 5.
- EThe distance between and is less than 5.

**Q10: **

Find the solution set of the inequality .

- A
- B
- C
- D
- E

**Q11: **

Find algebraically the solution set of the inequality .

- A
- B
- C
- D

**Q12: **

Find the solution set of the inequality .

- A
- B
- C
- D
- E

**Q13: **

Suppose that and . Which of the following is true?

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- D
- E

**Q14: **

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

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- E

**Q16: **

Solve .

- A
- B
- C no solution
- Dany number
- E

**Q17: **

What is the interval which represents the set of all real numbers that are less than or equal to?

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- B
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- D

**Q18: **

Which of the following is true?

- A
- B
- C

**Q19: **

Find algebraically the solution set of the inequality .

- A
- B
- C
- D

**Q20: **

Find algebraically the solution set of the inequality .

- A
- B
- C
- D

**Q21: **

Use the graph to find the solution set of the inequality .

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- D