# How do you graph and solve |x + 4| <= 6?

Oct 16, 2017

See a solution process below:

#### Explanation:

The absolute value function takes any term and transforms it to its non-negative form. Therefore, we must solve the term within the absolute value function for both its negative and positive equivalent.

We can solve the problem using this system of inequalities:

$- 6 \le x + 4 \le 6$

$- 6 - \textcolor{red}{4} \le x + 4 - \textcolor{red}{4} \le 6 - \textcolor{red}{4}$

$- 10 \le x + 0 \le 2$

$- 10 \le x \le 2$

Or

$x \ge 10$ and $x \le 2$

Or, in interval notation:

$\left[- 10 , 2\right]$

To graph this we will draw two vertical lines at $- 10$ and $2$ on the horizontal axis.

The lines will be a solid line because the inequality operators contain an "or equal to" clause.

We will shade between the lines because the interval notation shows a space between the two lines: