# How do you solve 2( w - 7) - 1= - 3( - 8w + 3) - 7w?

May 31, 2017

$w = \frac{10}{3}$ or $w = 3 \frac{1}{3}$ or $w = 3.33 \overline{3}$

#### Explanation:

Step 1. Distribute the $2$ and $- 3$ into the parenthesis.

$\textcolor{red}{2} \left(w - 7\right) - 1 = \textcolor{red}{- 3} \left(- 8 w + 3\right) - 7 w$

$2 w - 14 - 1 = 24 - 9 - 7 w$

Step 2. Add the like terms, $w$s with $w$s and numbers with numbers.

$2 w - 15 = 15 - 7 w$

Add $15$ to both sides
$2 w - 15 + \textcolor{red}{15} = 15 - 7 w + \textcolor{red}{15}$
$2 w = 30 - 7 w$

Add $7 w$ to both sides
$2 w + \textcolor{red}{7 w} = 30 - 7 w + \textcolor{red}{7 w}$
$9 w = 30$

Divide both sides by $9$
$\frac{\cancel{9} w}{\cancel{\textcolor{red}{9}}} = \frac{30}{\textcolor{red}{9}}$
$w = \frac{10}{3}$ or $w = 3 \frac{1}{3}$ or $w = 3.33 \overline{3}$