Q5. - 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 3 and less than -3.

Step-by-Step Solution

Answer

The absolute value inequality for all numbers greater than 3 and less than -3 is $\left|x\right|>3$.

Step 1 -Write the inequalities

Let the numbers are denoted by $x$. 

The inequality for the numbers greater than 3 is $x>3$.

The inequality for the numbers less than 3 is $x<-3$.

Step 2 &ndash; The absolute value inequality

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

Therefore, the absolute value inequality for the numbers greater than 3 and less than -3 is $x>3$and $x<-3$.

$\left|x\right|>3$

Step 3 &ndash; Graph of the solution set

The graph for the absolute inequality is $\left|x\right|>3$ as shown below