Q20. - Algebra 2

Question

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

20. all numbers less than or equal to  $1.2$ and greater than or equal to  $-1.2$

Step-by-Step Solution

Answer

Absolute value inequality is $\left|x\right|\le 1.2$ 

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 $x\le 1.2\text{ and }x\ge -1.2$ so from definition, absolute value inequality is 

$\left|x\right|\le 1.2$ 

Step 3 - Graph the solution set

For $x\le 1.2\text{ and }x\ge -1.2$, number line starts from -1.2 to 1.2

Dot on $-1.2\text{ and }1.2$ shows these points are included in the solution.