Question

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

33. $\left|g\right|\le 9$

Short answer

Solution of inequality is $-9\le g\le 9$

Solution set in number line is

Step-by-step solution

- Definition of absolute value inequality

For real numbers $a\text{and}b$ with $b>0$

Absolute value inequality is $\left|a\right|<b$ when $-b<a\text{and}a<b$, and

Absolute value inequality is $\left|a\right|>b$ when $a<-b\text{or}a>b$

- Simplify g≤9

From definition of absolute value inequality, given expression is simplified to

$-9\le g\le 9$

- Graph the solution set

For $g\ge -9\text{and}g\le 9$, number line starts from $-9$ to 9

Dot on $-9\text{and}9$ shows these points are included in the solution.