Q33. - Algebra 2

Question

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

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

Step-by-Step Solution

Answer

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

Solution set in number line is

Step 1 - 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 $a<-b\text{ or }a>b$ 

Step 2 - Simplify g &#8804; 9

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

$-9\le g\le 9$  

Step 3 - 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.