# How do you solve 4(4 - w) = 3(2w + 2) ?

Mar 27, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms in parenthesis by multiplying each term within the parenthesis by the term outside the parethesis:

$\textcolor{red}{4} \left(4 - w\right) = \textcolor{b l u e}{3} \left(2 w + 2\right)$

$\left(\textcolor{red}{4} \times 4\right) - \left(\textcolor{red}{4} \times w\right) = \left(\textcolor{b l u e}{3} \times 2 w\right) + \left(\textcolor{b l u e}{3} \times 2\right)$

$16 - 4 w = 6 w + 6$

Next, add $\textcolor{red}{4 w}$ and subtract $\textcolor{b l u e}{6}$ from each side of the equation to isolate the $w$ terms while keeping the equation balanced:

$16 - 4 w + \textcolor{red}{4 w} - \textcolor{b l u e}{6} = 6 w + 6 + \textcolor{red}{4 w} - \textcolor{b l u e}{6}$

$16 - \textcolor{b l u e}{6} - 4 w + \textcolor{red}{4 w} = 6 w + \textcolor{red}{4 w} + 6 - \textcolor{b l u e}{6}$

$10 - 0 = \left(6 + \textcolor{red}{4}\right) w + 0$

$10 = 10 w$

$\frac{10}{\textcolor{red}{10}} = \frac{10 w}{\textcolor{red}{10}}$

$1 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{10}}} w}{\cancel{\textcolor{red}{10}}}$

$1 = w$

$w = 1$