Q7. - Algebra 2

Question

Write an absolute value inequality.

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|<2$

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 $-2$ and less than 2

Step 3 - Write absolute value inequality

Let the real number be $x$ 

As $x>-2\text{ and }x<2$ so from definition, absolute value inequality is 

$\left|x\right|<2$