# How do you solve for m in 10m-p = -n + p m?

Jul 25, 2016

#### Answer:

color(green)(m=(p-n)/(10-p)

#### Explanation:

Given
$\textcolor{w h i t e}{\text{XXX}} 10 m - p = - n + p m$

We need to get all the terms involving $m$ on one side and all other terms on the other side:
$\textcolor{w h i t e}{\text{XXX}} 10 m - p \cdot m = p - n$

Extract the factor of $m$ from the terms on the left side
$\textcolor{w h i t e}{\text{XXX}} m \left(10 - p\right) = p - n$

(Assuming $p \ne 10$) divide both sides by $\left(10 - p\right)$ isolating a single $m$ on the left side
$\textcolor{w h i t e}{\text{XXX}} m = \frac{p - n}{10 - p}$