Q57. - Algebra 2

Question

Write an absolute value inequality for each graph

57. 

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 greater than 0 and less than 2

Step 3 - Write absolute value inequality

Let the real number be x

As $x>0\text{ and }x<2$

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

Subtract 1 on both sides

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

So from definition, absolute value inequality is 

$\left|x-1\right|<1$