# How do you graph the inequality  -6 <x + 3 < 6 ?

Oct 2, 2017

See a solution process below:

#### Explanation:

First, we need to solve to $x$. Subtract $\textcolor{red}{3}$ from each segment of the system of inequalities to solve for $x$ while keeping the system balanced:

$- 6 - \textcolor{red}{3} < x + 3 - \textcolor{red}{3} < 6 - \textcolor{red}{3}$

$- 9 < x + 0 < 3$

$- 9 < x < 3$

Or

$x > - 9$ and $x < 3$

To graph this we will draw vertical lines at $- 9$ and $3$ on the horizontal axis.

The lines will be a daashed because the inequality operators do not contain an "or equal to" clause.

We will shade between the two lines: