# How do you solve 3/10 - w = 4/5 - 3/5w?

Apr 4, 2016

$w = - \frac{5}{4}$

#### Explanation:

$1$. Add $\frac{3}{5} w$ to both sides of the equation.

$\frac{3}{10} - w = \frac{4}{5} - \frac{3}{5} w$

$\frac{3}{10} - w$ $\textcolor{red}{+ \frac{3}{5} w} = \frac{4}{5} - \frac{3}{5} w$ $\textcolor{red}{+ \frac{3}{5} w}$

$2$ Rewrite $- w$ on the left side of the equation with a denominator of $5$.

$\frac{3}{10} - \frac{1}{1} w + \frac{3}{5} w = \frac{4}{5}$

$\frac{3}{10} - \frac{1 \textcolor{b l u e}{\times 5}}{1 \textcolor{b l u e}{\times 5}} w + \frac{3}{5} w = \frac{4}{5}$

$\frac{3}{10} - \frac{5}{5} w + \frac{3}{5} w = \frac{4}{5}$

$3$. Calculate $- \frac{5}{5} w + \frac{3}{5} w$.

$\frac{3}{10} - \frac{5 + 3}{5} w = \frac{4}{5}$

$\frac{3}{10} - \frac{2}{5} w = \frac{4}{5}$

$4$. Subtract $\frac{3}{10}$ from both sides of the equation.

$\frac{3}{10}$ $\textcolor{red}{- \frac{3}{10}} - \frac{2}{5} w = \frac{4}{5}$ $\textcolor{red}{- \frac{3}{10}}$

$5$. Rewrite $\frac{4}{5}$ on the right side of the equation with a denominator of $10$.

$- \frac{2}{5} w = \frac{4}{5} - \frac{3}{10}$

$- \frac{2}{5} w = \frac{4 \textcolor{b l u e}{\times 2}}{5 \textcolor{b l u e}{\times 2}} - \frac{3}{10}$

$- \frac{2}{5} w = \frac{8}{10} - \frac{3}{10}$

$6$. Calculate $\frac{8}{10} - \frac{3}{10}$.

$- \frac{2}{5} w = \frac{8 - 3}{10}$

$- \frac{2}{5} w = \frac{5}{10}$

$7$. Divide both sides of the equation by $- \frac{2}{5}$.

$- \frac{2}{5} w \textcolor{red}{\div - \frac{2}{5}} = \frac{5}{10} \textcolor{red}{\div - \frac{2}{5}}$

$8$. Solve for $w$.

$w = \frac{5}{10} \times - \frac{5}{2}$

$w = \frac{5}{10 \textcolor{b l u e}{\div 5}} \times - \frac{5 \textcolor{b l u e}{\div 5}}{2}$

$w = \frac{5}{2} \times - \frac{1}{2}$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} w = - \frac{5}{4} \textcolor{w h i t e}{\frac{a}{a}} |}}}$