Question

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

$\left|g+4\right|\le 9$.

Short answer

The solution of the given inequality is $-13\le g\le 5$.

Step-by-step solution

-Write the inequalities 

A For all real numbers a, b and $b>0$; it is true that if $\left|a\right|\le b$then $-b<a<b$. The given absolute inequality is$\left|g+4\right|\le 9$.

– Apply the definition of an absolute compound inequality

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

$\begin{array}{c}|g+4|\le 9\\ -9\le g+4\le 9\\ -9-4\le g+4-4\le 9-4\\ -13\le g\le 5\end{array}$

Therefore, the solution of the given absolute inequality is $-13\le g\le 5$

– Graph of the solution set 

The graph for the inequality $-13\le g\le 5$is as shown below