# How do you solve and write the following in interval notation: | 2x – 4 | ≤ 12?

Apr 28, 2017

See the entire solution process below:

#### Explanation:

The absolute value function takes any term, negative or positive, and transforms it to its positive form. Therefore, you need to solve the term inside the absolute value for both the positive and negative version of what it is equated to.

$- 12 \le 2 x - 4 \le 12$

$- 12 + \textcolor{red}{4} \le 2 x - 4 + \textcolor{red}{4} \le 12 + \textcolor{red}{4}$

$- 8 \le 2 x - 0 \le 16$

$- 8 \le 2 x \le 16$

$- \frac{8}{\textcolor{red}{2}} \le \frac{2 x}{\textcolor{red}{2}} \le \frac{16}{\textcolor{red}{2}}$

$- 4 \le \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}} \le 8$

$- 4 \le x \le 8$

Or

$x \ge - 4$ and $x \le 8$

Or, in interval notation

$\left[- 4 , 8\right]$