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

Oct 2, 2017

$\left(- 3 , 3\right)$

#### 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: $| 4 x | > - 12$ and $| - \left(4 x\right) | > - 12$

Remove bars:

$4 x > - 12 \implies x > - 3$

$- 4 x > - 12 \implies x < 3$

In interval notation this is:

$\left(- 3 , 3\right)$