# How do you solve 5+8abs(-10n-2)=101?

Sep 6, 2017

See a solution process below:

#### Explanation:

First, subtract $\textcolor{red}{5}$ from each side of the equation to isolate the absolute value term while keeping the equation balanced:

$5 - \textcolor{red}{5} + 8 \left\mid - 10 n - 2 \right\mid = 101 - \textcolor{red}{5}$

$0 + 8 \left\mid - 10 n - 2 \right\mid = 96$

$8 \left\mid - 10 n - 2 \right\mid = 96$

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

$\frac{8 \left\mid - 10 n - 2 \right\mid}{\textcolor{red}{8}} = \frac{96}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} \left\mid - 10 n - 2 \right\mid}{\cancel{\textcolor{red}{8}}} = 12$

$\left\mid - 10 n - 2 \right\mid = 12$

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:

$- 10 n - 2 = - 12$

$- 10 n - 2 + \textcolor{red}{2} = - 12 + \textcolor{red}{2}$

$- 10 n - 0 = - 10$

$- 10 n = - 10$

$\frac{- 10 n}{\textcolor{red}{- 10}} = \frac{- 10}{\textcolor{red}{- 10}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 10}}} n}{\cancel{\textcolor{red}{- 10}}} = 1$

$n = 1$

Solution 2:

$- 10 n - 2 = 12$

$- 10 n - 2 + \textcolor{red}{2} = 12 + \textcolor{red}{2}$

$- 10 n - 0 = 14$

$- 10 n = 14$

$\frac{- 10 n}{\textcolor{red}{- 10}} = \frac{14}{\textcolor{red}{- 10}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 10}}} n}{\cancel{\textcolor{red}{- 10}}} = - \frac{14}{10}$

$n = - \frac{14}{10}$

The Solutions Are: $n = 1$ and $n = - \frac{14}{10}$