# How do you solve  6(m - 2) + 14 = 3(m + 2) - 10 ?

Mar 11, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{6} \left(m - 2\right) + 14 = \textcolor{b l u e}{3} \left(m + 2\right) - 10$

$\left(\textcolor{red}{6} \times m\right) - \left(\textcolor{red}{6} \times 2\right) + 14 = \left(\textcolor{b l u e}{3} \times m\right) + \left(\textcolor{b l u e}{3} \times 2\right) - 10$

$6 m - 12 + 14 = 3 m + 6 - 10$

$6 m + 2 = 3 m - 4$

Next, subtract $\textcolor{red}{2}$ and $\textcolor{b l u e}{3 m}$ from each side of the equation to isolate the $m$ term while keeping the equation balanced:

$6 m + 2 - \textcolor{red}{2} - \textcolor{b l u e}{3 m} = 3 m - 4 - \textcolor{red}{2} - \textcolor{b l u e}{3 m}$

$6 m - \textcolor{b l u e}{3 m} + 2 - \textcolor{red}{2} = 3 m - \textcolor{b l u e}{3 m} - 4 - \textcolor{red}{2}$

$\left(6 - 3\right) m + 0 = 0 - 6$

$3 m = - 6$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $m$ while keeping the equation balanced:

$\frac{3 m}{\textcolor{red}{3}} = - \frac{6}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} m}{\cancel{\textcolor{red}{3}}} = - 2$

$m = - 2$