Chapter A.9, Problem 100AYU

To determine

To solve: Each inequality. Express your answer using set notation or interval notation. Graph the solution set.

Answer to Problem 100AYU

$\left\{x|x \le -3 or x \ge -1\right\}\text{ or }\left(-\infty , -3\right] \cup \left[-1, \infty \right)$

Explanation of Solution

$\begin{array}{l}|-x-2| \ge 1\hfill \\ |-\left(x + 2\right)| \ge 1\hfill \\ |x + 2| \ge 1\hfill \\ x + 2 \le -1\text{ or }x + 2 \ge 1\hfill \\ x + 2-2 \le -1-2\text{ or }x + 2-2 \ge 1-2\hfill \\ x \le -3\text{ or }x \ge -1\hfill \end{array}$

The solution set is $\left\{x|x \le -3 or x \ge 1\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , -3\right] \cup \left[1, \infty \right).$