Question 1

Which of the following is the correct interval notation for the solution set of the inequality $$|x| \u003e 4$$?

Accepted Answer

$$(−\infty,−4) \cup (4,\infty)$$

Question 2

Solve the inequality $$|2x-3| \leq 7$$ and express the solution in interval notation.

Accepted Answer

$$[−2,5]$$

Question 3

Which of the following compound inequalities is equivalent to $$|x+1| \u003c 6$$?

Accepted Answer

$$−6 \u003c x+1 \u003c 6$$

Question 4

What is the solution set for $$|x| \geq 3$$?

Accepted Answer

$$(−\infty,−3] \cup [3,\infty)$$

Question 5

Solve the inequality $$−2(3x−2) \geq 4−x$$ and give the solution in interval notation.

Accepted Answer

$$(−\infty,2]$$

Question 6

If $$|x| \u003c −5$$, what is the solution set?

Accepted Answer

$$\varnothing ($$the empty set)

Question 7

Which of the following represents the solution to $$|x−4| \geq 2$$?

Accepted Answer

$$(−\infty,2] \cup [6,\infty)$$

Question 8

Solve the compound inequality $$2x−3 \u003e 5$$ and $$4−x \leq 3. $$Express the solution in interval notation.

Accepted Answer

$$(4,7]$$

Question 9

Which of the following is the correct interval notation for the solution set of $$|x+2| \u003e 5$$?

Accepted Answer

$$(−\infty,−7) \cup (3,\infty)$$

Question 10

Given $$A = (−4,6]$$ and $$B = [2,10)$$, what is $$A \cap B$$?

Accepted Answer

$$[2,6]$$

Question 11

Solve the absolute value inequality $$|3x+2| \u003c 7$$ and give the solution in interval notation.

Accepted Answer

$$(−3,\frac{5}{3})$$

Question 12

Which of the following is the correct solution set for $$|x| \leq 8$$?

Accepted Answer

$$[−8,8]$$

Question 13

If $$|x−5| \leq 0$$, what is the solution set?

Accepted Answer

$$\{5\}$$

Question 14

Solve the inequality $$1/2(x+6) \u003e 3 or$$ $$4(x−1) \u003c 3x−4. $$Express the solution in interval notation.

Accepted Answer

$$(0,\infty)$$

Question 15

Which of the following is the correct interval notation for the solution set of $$−10 \u003c 2x−7 \leq 4$$?

Accepted Answer

$$(−1.5,5.5]$$

Linear and Absolute Value Inequalities: Study Guide

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