# How do you solve 9m+2=3m-10?

Dec 28, 2016

$m = - 2$

#### Explanation:

We need to subtract $\textcolor{red}{3 m}$ and $\textcolor{b l u e}{2}$ from each side of the equation. This will let us isolate the $m$ terms on one side of the equation and the constants on the other side of the equation while keeping the equation balanced:

$9 m + 2 - \textcolor{red}{3 m} - \textcolor{b l u e}{2} = 3 m - 10 - \textcolor{red}{3 m} - \textcolor{b l u e}{2}$

$9 m - \textcolor{red}{3 m} + 2 - \textcolor{b l u e}{2} = 3 m - \textcolor{red}{3 m} - 10 - \textcolor{b l u e}{2}$

$9 m - \textcolor{red}{3 m} + 0 = 0 - 10 - \textcolor{b l u e}{2}$

$9 m - \textcolor{red}{3 m} = - 10 - \textcolor{b l u e}{2}$

Next, we can combine like terms on each side of the equation:

$\left(9 - 3\right) m = - 12$

$6 m = - 12$

Now we can divide each side of the equation by $\textcolor{g r e e n}{6}$ to solve for $m$ and keep the equation balanced:

$\frac{6 m}{\textcolor{g r e e n}{6}} = - \frac{12}{\textcolor{g r e e n}{6}}$

$\frac{\textcolor{g r e e n}{\cancel{\textcolor{b l a c k}{6}}} m}{\cancel{\textcolor{g r e e n}{6}}} = - 2$

$m = - 2$