Q26. - Algebra 2

Question

 Write an absolute value inequality for each graph

26. 

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x-1\right|\le 3$

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 or equal to -2 and less than or equal to 4

Step 3 - Write absolute value inequality

Let the real number be x 

As $x\ge -2\text{ and }x\le 4$

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

Subtract 1 on both sides

$\begin{array}{c}x-1\ge -2-1\text{ and }x-1\le 4-1\\ x-1\ge -3\text{ and }x-1\le 3\end{array}$

So from definition, absolute value inequality is 

$|x-1|\le 3$