Q15. - 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 or equal to 5 or less than or equal to $-5$

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|\ge 5$

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 $x\ge 5\text{ or }x\le -5$ so from definition, absolute value inequality is

$\left|x\right|\ge 5$

Step 3 - Graph the solution set

For $x\ge 5\text{ or }x\le -5$, number line starts from 5 to $\infty$  and from -5 to $-\infty$

Dot on $5\text{ and }-5$ shows these points are included in the solution.