Q56. - Algebra 2

Question

Write an absolute value inequality for each graph.

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x+1\right|>2$

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$-3$ or greater than 1

Step 3 - Write absolute value inequality

Let the real number be x 

As $x<-3\text{ or }x>1$

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

Add 1 on both sides

$\begin{array}{c}x+1<-3+1\text{ or }x+1>1+1\\ x+1<-2\text{ or }x+1>2\end{array}$

 So from definition, absolute value inequality is 

$\left|x+1\right|>2$