# How do you solve -3/2 = -6/7v - 5/3?

Feb 14, 2017

See the entire solution process below:

#### Explanation:

First, multiply both sides of the equation by the lowest common denominator of the three fractions to eliminate the fractions while keeping the equation balanced. The LCD is $7 \times 3 \times 2 = \textcolor{red}{42}$

$\textcolor{red}{42} \times - \frac{3}{2} = \textcolor{red}{42} \left(- \frac{6}{7} v - \frac{5}{3}\right)$

$\textcolor{red}{42} \times - \frac{3}{2} = \left(\textcolor{red}{42} \times - \frac{6}{7} v\right) - \left(\textcolor{red}{42} \times \frac{5}{3}\right)$

$\cancel{\textcolor{red}{42}} 21 \times - \frac{3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}} = \left(\cancel{\textcolor{red}{42}} 6 \times - \frac{6}{\textcolor{red}{\cancel{\textcolor{b l a c k}{7}}}} v\right) - \left(\cancel{\textcolor{red}{42}} 14 \times \frac{5}{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}}}\right)$

$21 \times - 3 = \left(6 \times - 6 v\right) - \left(14 \times 5\right)$

$- 63 = - 36 v - 70$

Next, add $\textcolor{red}{70}$ to each side of the equation to isolate the $v$ term while keeping the equation balanced:

$- 63 + \textcolor{red}{70} = - 36 v - 70 + \textcolor{red}{70}$

$7 = - 36 v - 0$

$7 = - 36 v$

Now, divide each side of the equation by $\textcolor{red}{- 36}$ to solve for $v$ while keeping the equation balanced:

$\frac{7}{\textcolor{red}{- 36}} = \frac{- 36 v}{\textcolor{red}{- 36}}$

$- \frac{7}{36} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 36}}} v}{\cancel{\textcolor{red}{- 36}}}$

$- \frac{7}{36} = v$

$v = - \frac{7}{36}$