# How do you solve abs(-2n+6)=6?

Jan 7, 2017

Because this problem contains an absolute value we need to handle it differently than a regular equation. See full explanation below.

#### Explanation:

Because this problem contains an absolute value we need to handle it differently than a regular equation. The absolute value function transform any negative or positive term into its positive equivalent. Therefore we need to solve the term within the absolute value for both the negative and positive solution of the equation.

Solution 1)

$- 2 n + 6 = 6$

$- 2 n + 6 - \textcolor{red}{6} = 6 - \textcolor{red}{6}$

$- 2 n + 0 = 0$

$- 2 n = 0$

$\frac{- 2 n}{\textcolor{red}{- 2}} = \frac{0}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} n}{\cancel{\textcolor{red}{- 2}}} = 0$

$n = 0$

Solution 2)

$- 2 n + 6 = - 6$

$- 2 n + 6 - \textcolor{red}{6} = - 6 - \textcolor{red}{6}$

$- 2 n + 0 = - 12$

$- 2 n = - 12$

$\frac{- 2 n}{\textcolor{red}{- 2}} = - \frac{12}{\textcolor{red}{- 2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} n}{\cancel{\textcolor{red}{- 2}}} = 6$

$n = 6$