Q23. - Algebra 2

Question

Write an absolute value inequality for each graph

23. 

Step-by-Step Solution

Answer

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

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

Step 3 - 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 

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