Q19. - Algebra 2

Question

Write an absolute value inequality for each of the following. Then graph the solution set on a number line.

 all numbers greater than 8 or less than $-8$ 

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|>8$ 

Solution set in number line is

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 - Write an absolute value inequality

Let the real number be x 

As $x>8\text{ or }x<-8$ so from definition, absolute value inequality is 

$\left|x\right|>8$ 

Step 3 - Graph the solution set

For $x>8\text{ or }x<-8$, number line starts from -8 to $-\infty$ and from 8 to $\infty$

Open circle on $-8\text{ and }8$ shows these points are not included in the solution.