Question 1

Solve the absolute value equation: $$|2x - 5| = 9. $$What is the solution set?

Accepted Answer

$$x = 7,\ x = -2$$

Question 2

Which of the following is the correct solution to the equation $$|3x + 4| = 0$$?

Accepted Answer

$$x = -\dfrac{4}{3}$$

Question 3

A chemist needs to keep the temperature of a reaction within $$2$$ degrees of $$100^\circC. $$Which absolute value inequality represents this requirement?

Accepted Answer

$$|T - 100| \leq 2$$

Question 4

Solve the equation $$|x + 3| = |2x - 1|.$$

Accepted Answer

$$x = -4,\ x = 2$$

Question 5

Which of the following absolute value equations has no solution?

Accepted Answer

$$|x - 2| = -5$$

Question 6

A medical test result is considered normal if it is within $$1.5$$ units of the value $$7.0. $$Which interval represents all normal test results?

Accepted Answer

$$[5.5,\ 8.5]$$

Question 7

Solve the absolute value equation: $$|5 - 2x| = 3.$$

Accepted Answer

$$x = 1,\ x = 4$$

Question 8

Which of the following best describes the solution set of $$|x| \u003c 7$$?

Accepted Answer

$$(-7,\ 7)$$

Question 9

If $$|x - 4| = 12$$, what are the solutions for $$x$$?

Accepted Answer

$$x = 16,\ x = -8$$

Question 10

A company requires that the deviation from the target weight of $$50$$ grams for a product must not exceed $$0.8$$ grams. Which absolute value inequality models this requirement?

Accepted Answer

$$|w - 50| \leq 0.8$$

Question 11

Solve the equation $$|4x + 1| = 7.$$

Accepted Answer

$$x = 1.5,\ x = -2$$

Question 12

Which of the following is the correct solution set for $$|x + 2| = 5$$?

Accepted Answer

$$x = 3,\ x = -7$$

Question 13

A historical event occurred in the year $$x$$, and it is known to have happened within $$10$$ years of $$1950. $$Which absolute value equation represents this information?

Accepted Answer

$$|x - 1950| \leq 10$$

Question 14

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

Accepted Answer

No solution

Question 15

Which of the following is the solution set for $$|2x| = 8$$?

Accepted Answer

$$x = 4,\ x = -4$$

Question 16

A car's speed $$v$$ must not differ from $$60$$ mph by more than $$5$$ mph. Which absolute value inequality models this requirement?

Accepted Answer

$$|v - 60| \leq 5$$

Question 17

Solve the equation $$|x - 7| = 0.$$

Accepted Answer

$$x = 7$$

Question 18

Which of the following is the solution set for $$|x + 1| = 6$$?

Accepted Answer

$$x = 5,\ x = -7$$

Question 19

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

Accepted Answer

The empty set

Question 20

Solve the equation $$|3x - 2| = 11.$$

Accepted Answer

$$x = \dfrac{13}{3},\ x = -3$$

Question 21

Which of the following is the solution set for $$|x| = 0$$?

Accepted Answer

$$x = 0$$

College Algebra Study Guide: Absolute Value Equations

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