# How do you solve 3/4n + 16 = 2-1/8n ?

Jul 25, 2016

$\textcolor{g r e e n}{n = - 16}$

#### Explanation:

Given:
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{\frac{3}{4} n + 16} = \textcolor{b l u e}{2 - \frac{1}{8} n}$

Get all terms with $n$ as a factor on the left side
color(white)("XXX")color(red)(3/4n+16)color(blue) (+1/8n)=color(blue)(2)

Get all the terms that do not have $n$ as a factor on the right side
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{\frac{3}{4} n} \textcolor{b l u e}{+ \frac{1}{8} n} = \textcolor{b l u e}{2} \textcolor{red}{- 16}$

Simplify both sides
$\textcolor{w h i t e}{\text{XXX}} \frac{7}{8} n = - 14$

Multiply both sides by $\frac{8}{7}$ to leave a unit $n$ on the left side
$\textcolor{w h i t e}{\text{XXX}} n = - 16$

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As always, you should verify this answer by substituting the result into the original equation.