# How do you solve |6h|<12?

Jan 9, 2017

See full explanation below.

#### Explanation:

Because this problem contains an absolute value function we must solve this problem for both -12 and +12.

Also, because it is an inequality we must solve a system on inequalities and not just a single equation.

We can rewrite this problem as:

$- 12 < 6 h < 12$

Now we can divide each portion of the system by $\textcolor{red}{6}$ to solve for $h$ while keeping the system balanced:

$- \frac{12}{\textcolor{red}{6}} < \frac{6 h}{\textcolor{red}{6}} < \frac{12}{\textcolor{red}{6}}$

$- 2 < \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}} h}{\cancel{\textcolor{red}{6}}} < 2$

$- 2 < h < 2$