Question

Write an absolute value inequality for each graph

26.

Short answer

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

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

- 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

$|x-1|\le 3$