# How do you solve 8|12x + 7| = 80?

Sep 4, 2017

See a solution process below:

#### Explanation:

First, divide each side of the equation by $\textcolor{red}{8}$ to isolate the absolute value function while keeping the equation balanced:

$\frac{8 \left\mid 12 x + 7 \right\mid}{\textcolor{red}{8}} = \frac{80}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} \left\mid 12 x + 7 \right\mid}{\cancel{\textcolor{red}{8}}} = 10$

$\left\mid 12 x + 7 \right\mid = 10$

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.

Solution 1:

$12 x + 7 = - 10$

$12 x + 7 - \textcolor{red}{7} = - 10 - \textcolor{red}{7}$

$12 x + 0 = - 17$

$12 x = - 17$

$\frac{12 x}{\textcolor{red}{12}} = - \frac{17}{\textcolor{red}{12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} x}{\cancel{\textcolor{red}{12}}} = - \frac{17}{12}$

$x = - \frac{17}{12}$

Solution 2:

$12 x + 7 = 10$

$12 x + 7 - \textcolor{red}{7} = 10 - \textcolor{red}{7}$

$12 x + 0 = 3$

$12 x = 3$

$\frac{12 x}{\textcolor{red}{12}} = \frac{3}{\textcolor{red}{12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} x}{\cancel{\textcolor{red}{12}}} = \frac{1}{4}$

$x = \frac{1}{4}$

The Solutions Are: $x = - \frac{17}{12}$ and $x = \frac{1}{4}$