Question

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

All numbers less than 7 and greater than $-7$

Short answer

Absolute value inequality is $\left|x\right|<7$

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 $x>-7\text{and}x<7$ so from definition, absolute value inequality is

$\left|x\right|<7$

- Graph the solution set

For$x>-7\text{and}x<7$, number line starts from -7 to 7

Open circle on $\text{7 and}-7$shows these points are not included in the solution.