# How do you solve  |3n-2|=1/2?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

This problem contains the absolute value function. The absolute value function transforms any negative or positive term into its positive form. Therefore, we must solve the term within the absolute value for both its negative and positive equivalent.

Solution 1)
$3 n - 2 = - \frac{1}{2}$

$3 n - 2 + \textcolor{red}{2} = - \frac{1}{2} + \textcolor{red}{2}$

$3 n - 2 + \textcolor{red}{2} = - \frac{1}{2} + \left(\frac{2}{2} \times \textcolor{red}{2}\right)$

$3 n - 0 = - \frac{1}{2} + \frac{4}{2}$

$3 n = \frac{3}{2}$

$\frac{3 n}{\textcolor{red}{3}} = \frac{3}{2} \times \frac{1}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} n}{\cancel{\textcolor{red}{3}}} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}{2} \times \frac{1}{\cancel{\textcolor{red}{3}}}$

$n = \frac{1}{2}$

Solution 2)
$3 n - 2 = \frac{1}{2}$

$3 n - 2 + \textcolor{red}{2} = \frac{1}{2} + \textcolor{red}{2}$

$3 n - 2 + \textcolor{red}{2} = \frac{1}{2} + \left(\frac{2}{2} \times \textcolor{red}{2}\right)$

$3 n - 0 = \frac{1}{2} + \frac{4}{2}$

$3 n = \frac{5}{2}$

$\frac{3 n}{\textcolor{red}{3}} = \frac{5}{2} \times \frac{1}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} n}{\cancel{\textcolor{red}{3}}} = \frac{5}{6}$

$n = \frac{5}{6}$

The solutions are $n = \frac{1}{2}$ and $n = \frac{5}{6}$