# How do you solve abs(6n+1)=1/2?

Jun 14, 2017

$n = - \frac{1}{12}$ and $n = - \frac{1}{4}$

#### Explanation:

Since absolute value bars are involved, you know that the quantity $\left(6 n + 1\right)$ *within the bars will always end up positive.*

Therefore, $\left(6 n + 1\right)$ can be equal to $\frac{1}{2}$ OR $- \frac{1}{2}$. There are two possible solutions for n.

You must set up and solve 2 separate equations to solve for the positive and negative versions.
First Equation: quantity in absolute value bars equal to $\frac{1}{2}$.
$\left(6 n + 1\right) = \frac{1}{2}$ [Solve]
$n = - \frac{1}{12}$
Second Equation: quantity in absolute value bars equal to $- \frac{1}{2}$.
$\left(6 n + 1\right) = - \frac{1}{2}$ [Solve]
$n = - \frac{1}{4}$

Both $- \frac{1}{12}$ and $- \frac{1}{4}$ are solutions to $| 6 n + 1 | = \frac{1}{2}$.

If you want to check your work, SEPARATELY substitute these solutions for $n$ into the original equation, $| 6 n + 1 | = \frac{1}{2}$.