# How do you solve |5x + 11| = 6?

##### 1 Answer
Oct 9, 2017

See a solution process below: $x = - \frac{17}{5}$ and $x = - 1$

#### 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.

Solution 1:

$5 x + 11 = - 6$

$5 x + 11 - \textcolor{red}{11} = - 6 - \textcolor{red}{11}$

$5 x + 0 = - 17$

$5 x = - 17$

$\frac{5 x}{\textcolor{red}{5}} = - \frac{17}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - \frac{17}{5}$

$x = - \frac{17}{5}$

Solution 2:

$5 x + 11 = 6$

$5 x + 11 - \textcolor{red}{11} = 6 - \textcolor{red}{11}$

$5 x + 0 = - 5$

$5 x = - 5$

$\frac{5 x}{\textcolor{red}{5}} = - \frac{5}{\textcolor{red}{5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} x}{\cancel{\textcolor{red}{5}}} = - 1$

$x = - 1$

The Solutions Are: $x = - \frac{17}{5}$ and $x = - 1$