Question

Write an absolute value inequality for each graph

23.

Short answer

Absolute value inequality is $\left|x\right|\ge 1.5$

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 less than or equal to -1.5 or greater than or equal to 1.5

- Write absolute value inequality

Let the real number be x

As $x\le -1.5\text{or}x\ge 1.5$ so from definition, absolute value inequality is

$\left|x\right|\ge 1.5$