Q16. - Algebra 2

Question

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

All numbers less than 7 and greater than $-7$

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|<7$ 

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 $x>-7\text{ and }x<7$ so from definition, absolute value inequality is

$\left|x\right|<7$ 

Step 3 - Graph the solution set

For $x>-7\text{ and }x<7$, number line starts from -7 to 7

Open circle on $\text{7 and }-7$ shows these points are not included in the solution.