# How do you solve n-10=5/6n-7-1/3n?

Nov 7, 2016

$n = 6$

#### Explanation:

Step 1) Get all of the terms containing $n$ over a common denominator by multiplying the term by the necessary for of $1$.
Step 2) Solve for $n$ while keeping the equation balanced

$\left(\frac{6}{6}\right) n - 10 = \left(\frac{5}{6}\right) n - 7 - \left(\frac{2}{2}\right) \left(\frac{1}{3}\right) n$

$\frac{6 n}{6} - 10 = \frac{5 n}{6} - 7 - \frac{2 n}{6}$

$\frac{6 n}{6} - 10 = \frac{3 n}{6} - 7$

$\frac{6 n}{6} - 10 + 10 - \frac{3 n}{6} = \frac{3 n}{6} - 7 + 10 - \frac{3 n}{6}$

$\frac{6 n}{6} - \frac{3 n}{6} = 3$

$\frac{3 n}{6} = 3$

$\left(\frac{6}{3}\right) \left(\frac{3 n}{6}\right) = \left(\frac{6}{3}\right) 3$

$n = 6$