Question

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

All numbers greater than 3 and less than -3.

Short answer

The absolute value inequality for all numbers greater than 3 and less than -3 is $\left|x\right|>3$.

Step-by-step solution

-Write the inequalities 

Let the numbers are denoted by $x$.

The inequality for the numbers greater than 3 is $x>3$.

The inequality for the numbers less than 3 is $x<-3$.

– The absolute value inequality

The absolute inequality is defined as $\left|x\right|>a$ for $\left|x\right|>a$and $x<-a$.

Therefore, the absolute value inequality for the numbersgreater than 3 and less than -3 is $x>3$and $x<-3$.

$\left|x\right|>3$

– Graph of the solution set 

The graph for the absolute inequality is $\left|x\right|>3$as shown below