Chapter A.9, Problem 99AYU

To determine

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

Answer to Problem 99AYU

$\left\{x|x \le -2 or x \ge 2\right\}\text{ or }\left(-\infty , -2\right] \cup \left[2, \infty \right)$

Explanation of Solution

$\begin{array}{l}|-2x| \ge |-4|\hfill \\ \left|2x\right| \ge 4\hfill \\ 2x \le -4\text{ or }2x \ge 4\hfill \\ \frac{2x}{2} \le -4\text{ or }\frac{2x}{2} \ge \frac{4}{2}\hfill \\ x \le -2\text{ or }x \ge 2\hfill \end{array}$

The solution set is $\left\{x|x \le -2 or x \ge 2\right\}$ or using interval notation, all numbers in the interval $\left(-\infty , -2\right] \cup \left[2, \infty \right).$