Q13. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

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

Step 1 -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 $\left|w\right|\ge -2$. 

Step 2 &ndash; 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:

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

Step 3 &ndash; Graph of the solution set

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