# Worksheet: Absolute Value Inequalities

Q1:

Find the solution set of the inequality .

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• B
• C
• D
• E

Q2:

Find the solution set of the inequality .

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• B
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• D
• E

Q3:

Find the solution set of the inequality .

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• D
• E

Q4:

Find the solution set of the inequality .

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• E

Q5:

Find the solution set of the inequality .

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• D
• E

Q6:

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

Q7:

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 centimeters, determine the time interval during which the body is less than 9 cm from .

• A
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• D

Q8:

Solve .

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Q9:

Suppose that and . Which of the following is true?

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• E

Q10:

Find algebraically the solution set of the inequality .

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• D

Q11:

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

Q12:

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.

Q13:

Solve .

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

Q14:

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

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• D
• E

Q15:

Which of the following is true?

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• B
• C

Q16:

Find algebraically the solution set of the inequality .

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• D

Q17:

Find algebraically the solution set of the inequality .

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• D

Q18:

Find algebraically the solution set of the inequality .

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• B
• C
• D

Q19:

Find algebraically the solution set of the inequality .

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• B
• C
• D

Q20:

Find the solution set of the inequality .

• A
• B
• C
• D
• E

Q21:

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

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• D

Q22:

Find algebraically the solution set of the inequality .

• A
• B
• C
• D

Q23:

Find the solution set of the inequality .

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• D
• E