# How do you solve |(3x - 5) / 6| > 4?

Nov 12, 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.

$- 4 > \frac{3 x - 5}{6} > 4$

First, multiply each segment of the system of inequalities by $\textcolor{red}{6}$ to eliminate the fraction while keeping the system balanced:

$\textcolor{red}{6} \times - 4 > \textcolor{red}{6} \times \frac{3 x - 5}{6} > \textcolor{red}{6} \times 4$

$- 24 > \cancel{\textcolor{red}{6}} \times \frac{3 x - 5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}} > 24$

$- 24 > 3 x - 5 > 24$

Next, add $\textcolor{red}{5}$ to each segment to isolate the $x$ term while keeping the system balanced:

$- 24 + \textcolor{red}{5} > 3 x - 5 + \textcolor{red}{5} > 24 + \textcolor{red}{5}$

$- 19 > 3 x - 0 > 29$

$- 19 > 3 x > 29$

Now, divide each segment by $\textcolor{red}{3}$ to solve for $x$ while keeping the system balanced:

$- \frac{19}{\textcolor{red}{3}} > \frac{3 x}{\textcolor{red}{3}} > \frac{29}{\textcolor{red}{3}}$

$- \frac{19}{3} > \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} > \frac{29}{3}$

$- \frac{19}{3} > x > \frac{29}{3}$

Or

$x < - \frac{19}{3}$ and $x > \frac{29}{3}$

Or, in interval notation:

$\left(- \infty , - \frac{19}{3}\right)$ and $\left(\frac{29}{3.} + \infty\right)$