Question 1

Solve the equation $$3|x + 5| = 12.$$

Accepted Answer

$$x = -1 or$$ $$x = -9$$

Question 2

Which of the following is the correct way to rewrite $$|u| = c$$ for $$c \u003e 0$$?

Accepted Answer

$$u = c or$$ $$u = -c$$

Question 3

Solve the equation $$|2x - 3| = 7.$$

Accepted Answer

$$x = 5 or$$ $$x = -2$$

Question 4

Solve the inequality $$|x - 2| \leq 5$$ and express the solution in interval notation.

Accepted Answer

$$[-3, 7]$$

Question 5

Which of the following best describes the solution set for $$|x + 4| \u003e 3$$?

Accepted Answer

$$x  -1$$

Question 6

If $$|u| \u003c 0$$, what is the solution set?

Accepted Answer

No solution

Question 7

Solve the inequality $$|2x + 1| \geq 9.$$

Accepted Answer

$$x \leq -5 or$$ $$x \geq 4$$

Question 8

A machine part is supposed to be 9.4 cm long with a tolerance of 0.01 cm. Which absolute value inequality represents the acceptable lengths $$x$$?

Accepted Answer

$$|x - 9.4| \leq 0.01$$

Question 9

Given the inequality $$|x - 3| \u003c 2$$, what is the solution set?

Accepted Answer

$$1 \u003c x \u003c 5$$

Question 10

A poll shows 41% of adults dread going to the dentist with a margin of error of 3.2%. Which interval represents the possible true percentage?

Accepted Answer

$$[37.8\%, 44.2\%]$$

Question 11

Solve $$|x| = -4.$$

Accepted Answer

No solution

Question 12

Which of the following is the correct solution to $$|x + 2| \geq 5$$?

Accepted Answer

$$x \leq -7 or$$ $$x \geq 3$$

Question 13

If $$|x - 1| \u003c 0$$, what is the solution set?

Accepted Answer

No solution

Question 14

Solve $$|3x - 6| = 0.$$

Accepted Answer

$$x = 2$$

Question 15

Which of the following is the correct solution to $$|x| \leq 4$$?

Accepted Answer

$$-4 \leq x \leq 4$$

Question 16

Solve the inequality $$|x + 1| \u003e 6.$$

Accepted Answer

$$x  5$$

Question 17

Which of the following is always true for any real number $$x$$?

Accepted Answer

$$|x| \geq 0$$

Question 18

A temperature sensor is accurate within $$\pm 2$$ degrees of the true temperature $$T. $$Which inequality represents the possible readings $$x$$?

Accepted Answer

$$|x - T| \leq 2$$

Question 19

Solve $$|4x + 8| \u003c 12.$$

Accepted Answer

$$-5 \u003c x \u003c 1$$

Absolute Value Equations and Inequalities: College Algebra Study Guide

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