Q4. - Algebra 2

Question

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

All numbers are between -8 and 8.

Step-by-Step Solution

Answer

The absolute value inequality for all numbers between -8 and 8 is $\left|x\right|<8$

Step 1 -Write the inequalities

Let the numbers are denoted by $x$ between -8 and 8.

The inequalities for the numbers between -8 and 8 are as follows:

$x>-8$

and

$x<8$

 Therefore, the compound inequality will be $-8<x<8$.

Step 2 &ndash; The absolute value inequality

The absolute inequality is defined as $\left|x\right|<a$ for $-a<x<a$.

Therefore, the absolute value inequality for the numbers between -8 and 8 is as follows:

$x>-8$

and

$x<8$

$\left|x\right|<8$

Step 3 &ndash; Graph of the solution set

The graph for the absolute inequality $\left|x\right|<8$ is as shown below