# How do you solve 2/9w-1/4=5/6?

Mar 2, 2017

Sere the entire solution process below:

#### Explanation:

First, multiply each side of the equation by $\textcolor{red}{36}$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{36} \left(\frac{2}{9} w - \frac{1}{4}\right) = \textcolor{red}{36} \times \frac{5}{6}$

$\left(\textcolor{red}{36} \times \frac{2}{9} w\right) - \left(\textcolor{red}{36} \times \frac{1}{4}\right) = \cancel{\textcolor{red}{36}} 6 \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{6}}}}$

(cancel(color(red)(36))4 xx 2/color(red)(cancel(color(black)(9)))w) - (cancel(color(red)(36))9 xx 1/color(red)cancel(color(black)(4)))) = 30

$8 w - 9 = 30$

Next, add $\textcolor{red}{9}$ to each side of the equation to isolate the $w$ term while keeping the equation balanced:

$8 w - 9 + \textcolor{red}{9} = 30 + \textcolor{red}{9}$

$8 w - 0 = 39$

$8 w = 39$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $w$ while keeping the equation balanced:

$\frac{8 w}{\textcolor{red}{8}} = \frac{39}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} w}{\cancel{\textcolor{red}{8}}} = \frac{39}{8}$

$w = \frac{39}{8}$