Q25. - Algebra 2

Question

Write an absolute value inequality for each graph

Step-by-Step Solution

Answer

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

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 - Observation from image

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

Step 3 - 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 

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