# How do you solve  2/3 v - 6 = 6 - 2/3 v ?

Jan 25, 2017

$v = 9$

#### Explanation:

$\frac{2}{3} v - 6 = 6 - \frac{2}{3} v$

$\frac{2}{3} v + \frac{2}{3} v = 6 + 6$

$\frac{4}{3} v = 12$

multiply with $\frac{3}{4}$

$\frac{3}{4} \cdot \frac{4}{3} v = \frac{3}{4} \cdot 12$

$v = 9$

Jan 25, 2017

See the entire solution process below:

#### Explanation:

First, add $\textcolor{red}{\frac{2}{3} v}$ and $\textcolor{b l u e}{6}$ to each side of the equation to isolate the $v$ terms and keep the equation balanced:

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

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

$\frac{4}{3} v - 0 = 12 - 0$

$\frac{4}{3} v = 12$

Now multiply each side of the equation by $\textcolor{red}{\frac{3}{4}}$ to solve for $v$ while keeping the equation balanced:

$\textcolor{red}{\frac{\cancel{3}}{\cancel{4}}} \times \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}}}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}} v = \frac{36}{4}$

$v = 9$