Question

Solve each inequality. Graph the solution set on a number line.

$\left|w\right|\ge -2$.

Short answer

The solution of the given inequality is $w>-2orw<2$.

Step-by-step solution

-Define absolute inequality and write the inequality

A For all real numbers a, b and $b>0$; it is true that if $\left|a\right|\ge b$then $a>b$ or $a<-b$. The inequality is $\left|w\right|\ge -2$.

– Apply the definition of an absolute compound inequality

Use the definition of absolute value inequality and write the compound inequality with word or as follows:

$\begin{array}{l}\left|w\right|\ge -2\\ w>-2orw<-(-2)\\ w>-2orw<2\end{array}$

– Graph of the solution set 

The graph for the inequalities $w>-2orw<2$ is as shown below