Question 1

Which of the following best describes the graph of $$y = |f(x)|$$ compared to $$y = f(x)$$?

Accepted Answer

It is a reflection of the portion of $$y = f(x)$$ below the x-axis across the x-axis.

Question 2

Solve the equation $$\left| \frac{1}{2}x + 1 \right| = 5.$$

Accepted Answer

$$x = 8$$ and $$x = -12$$

Question 3

Which of the following absolute value equations has no solution?

Accepted Answer

$$|5 + 3x| = -4$$

Question 4

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

Accepted Answer

$$x = -\frac{1}{2}$$ and $$x = \frac{3}{2}$$

Question 5

A cylindrical can must have a diameter $$D$$ such that $$|D - 3| \leq 0.02. $$What is the range of acceptable values for $$D$$?

Accepted Answer

$$2.98 \leq D \leq 3.02$$

Question 6

Solve the equation $$|4 - 2x| = 8.$$

Accepted Answer

$$x = -2$$ and $$x = 6$$

Question 7

Which of the following is the correct solution set for $$|4 - x| \u003c 2$$?

Accepted Answer

$$2 \u003c x \u003c 6$$

Question 8

Solve the inequality $$|3x + 2| \u003e 1.$$

Accepted Answer

$$x  -\frac{1}{3}$$

Question 9

A phone's thickness $$A$$ must not vary from $$9.33 mm by $$more than $$0.02 mm. $$Which absolute value inequality models this requirement?

Accepted Answer

$$|A - 9.33| \u003c 0.02$$

Question 10

Solve the inequality $$|3 - 2x| \u003c 5$$ and express the solution in interval notation.

Accepted Answer

$$(-1, 4)$$

Question 11

Which of the following statements is true about the solution to $$|x| = a$$ where $$a \u003e 0$$?

Accepted Answer

The solution is $$x = a or$$ $$x = -a$$

Question 12

Solve the equation $$|2x - 5| = |1 + x|.$$

Accepted Answer

$$x = 6$$ and $$x = 4/3$$

Question 13

Which of the following is the correct solution set for $$|-3x + 1| \u003e 8$$?

Accepted Answer

$$x  3$$

Question 14

If $$|x - 4| = 0$$, what is the value of $$x$$?

Accepted Answer

$$x = 4$$

Question 15

A quality control engineer needs the length $$L of a $$part to be within $$0.05$$ units of $$10$$ units. Which interval describes the acceptable values for $$L$$?

Accepted Answer

$$9.95 \leq L \leq 10.05$$

Question 16

Which of the following is the correct way to solve $$|ax + b| = c$$ for $$c \u003e 0$$?

Accepted Answer

Set $$ax + b = c or$$ $$ax + b = -c$$ and solve both equations.

Question 17

If $$|x - 2| \u003c 5$$, which of the following is the equivalent compound inequality?

Accepted Answer

$$-3 \u003c x \u003c 7$$

Question 18

A machine part must be manufactured so that its width $$W is no $$more than $$0.01$$ units away from $$5$$ units. Which absolute value inequality models this requirement?

Accepted Answer

$$|W - 5| \leq 0.01$$

Question 19

Which of the following is the solution set for $$|x + 3| \u003e 7$$?

Accepted Answer

$$x  4$$

Absolute Value Equations and Inequalities (Chapter 2.5) – College Algebra Study Notes

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