# How do you solve abs(5c-2)<=13?

Sep 22, 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.

$- 13 \le 5 c - 2 \le 13$

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

$- 13 + \textcolor{red}{2} \le 5 c - 2 + \textcolor{red}{2} \le 13 + \textcolor{red}{2}$

$- 11 \le 5 c - 0 \le 15$

$- 11 \le 5 c \le 15$

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

$- \frac{11}{\textcolor{red}{5}} \le \frac{5 c}{\textcolor{red}{5}} \le \frac{15}{\textcolor{red}{5}}$

$- \frac{11}{5} \le \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} c}{\cancel{\textcolor{red}{5}}} \le 3$

$- \frac{11}{5} \le c \le 3$

Or

$c \ge - \frac{11}{5}$ and $c \le 3$

Or, in interval notation:

$\left[- \frac{11}{5} , 3\right]$