Q18. - Algebra 2

Question

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

18. all numbers less than or equal to  $-6$ or greater than or equal to 6 

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|\ge 6$ 

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 $x\le -6\text{ or }x\ge 6$ so from definition, absolute value inequality is 

$\left|x\right|\ge 6$

Step 3 - Graph the solution set

For $x\le -6\text{ or }x\ge 6$, number line starts from -6 to $-\infty$ and from 6 to $\infty$

Dot on $-6\text{ and }6$ shows these points are included in the solution.