Question

How do you solve and write the following in interval notation: `| 4x | > -12`?

Answer 1

`(-3 , 3)`

Explanation:

To solve inequalities involing absolute values we need to solve for the case when the value in the absolute bars is both a positive value and a negative value. We can do this as follows:

If: `|4x| > -12` and `|-(4x)|> -12`

Remove bars:

`4x > -12 => x > -3`

`-4x > -12 => x< 3`

In interval notation this is:

`(-3 , 3)`