Question

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

Answer 1

See a solution process below:

Explanation:

First, we need to solve to `x`. Subtract `color(red)(3)` from each segment of the system of inequalities to solve for `x` while keeping the system balanced:

`-6 - color(red)(3) < x + 3 - color(red)(3) < 6 - color(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: