Question

Write an absolute value inequality for each graph

Short answer

Absolute value inequality is $\left|x+1\right|>1$

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

- Observation from image

From image, solution is all real less than -2 or greater than 0

- Write absolute value inequality

Let the real number be x

As $x<-2\text{or}x>0$

Since, adding same number on both sides does not change the sign of inequality

Add 1 on both sides

$\begin{array}{c}x+1<-2+1\text{or}x+1>0+1\\ x+1<-1\text{or}x+1>1\end{array}$

So from definition, absolute value inequality is

$\left|x+1\right|>1$