Section 1.8 Homework

1.  (a) The solution of the inequality |x| ≤ 2 is the interval ____

(b) The solution of the inequality |x| ≥ 2 is a union of two intervals ________

2.

(a) The set of all points on the real line whose distance from zero is less than 7 can be described by the absolute value inequality _______

(b) The set of all points on the real line whose distance from zero is greater than 7 can be described by the absolute value inequality ________

3.  Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

4. Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

2x − 5| = 9

5.  Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

6.  Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

7. Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

8.  Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

9.  Solve the equation. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

x =

10.  Solve the inequality. Express the answer using interval notation.

$\frac{1}{2}\left|x\right| \ge 4$

11. Solve the inequality. Express the answer using interval notation.

12.  Solve the inequality. Express the answer using interval notation.

13.  Solve the inequality. Express the answer using interval notation.

14. Solve the inequality. Express the answer using interval notation. 

$\left|\frac{x+5}{2}\right|\ge 6$

15.  Solve the inequality. Express the answer using interval notation.

16.  Solve the inequality. Express the answer using interval notation. 

$\frac{1}{2}\left|2x+1\right|>\frac{5}{6}$

17. A phrase that describes a set of real numbers is given. Express the phrase as an inequality involving an absolute value.

18 . A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set. 

19. A set of real numbers is graphed. Find an inequality involving an absolute value that describes the set. 

20.  A company manufactures industrial laminates (thin nylon-based sheets) of thickness 0.021 in., with a tolerance of 0.003 in.

(a) Find an inequality involving absolute values that describes the range of possible thickness for the laminate. (Use h for the thickness.) 

(b) Solve the inequality that you found in part (a). (Enter your answer using interval notation.)