# How do you graph and solve  |5x – 2|>=8?

Jul 27, 2018

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.

Therefore we can write and solve this as:

$- 8 \ge 5 x - 2 \ge 8$

First, add $\textcolor{red}{2}$ to each segment of the system of inequalities to isolate the $x$ term while keeping the system balanced:

$- 8 + \textcolor{red}{2} \ge 5 x - 2 + \textcolor{red}{2} \ge 8 + \textcolor{red}{2}$

$- 6 \ge 5 x - 0 \ge 10$

$- 6 \ge 5 x \ge 10$

Now, divide each segment by $\textcolor{red}{5}$ to solve for $x$ while keeping the system balanced:

$- \frac{6}{\textcolor{red}{5}} \ge \frac{5 x}{\textcolor{red}{5}} \ge \frac{10}{\textcolor{red}{5}}$

$- \frac{6}{5} \ge \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} \ge 2$

$- \frac{6}{5} \ge x \ge 2$

Or

$x \le - \frac{6}{5}$; $x \ge 2$

Or

$\left(- \infty , - \frac{6}{5}\right]$; $\left[2. + \infty\right)$