Question

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

all numbers greater than 8 or less than $-8$

Short answer

Absolute value inequality is $\left|x\right|>8$

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 $a<-b\text{or}a>b$

- Write an absolute value inequality

Let the real number be x

As $x>8\text{or}x<-8$ so from definition, absolute value inequality is

$\left|x\right|>8$

- Graph the solution set

For $x>8\text{or}x<-8$, number line starts from -8 to $-\infty$ and from 8 to $\infty$

Open circle on $-8\text{and}8$ shows these points are not included in the solution.