# How do you solve 10/5=(3v+10)/(v+4)?

Feb 10, 2017

See the entire solution process below:

#### Explanation:

First, multiply each side of the equation by the common denominator of the two fractions $\textcolor{red}{5} \textcolor{b l u e}{\left(v + 4\right)}$ to eliminate the fractions and keep the equation balanced:

$\textcolor{red}{5} \textcolor{b l u e}{\left(v + 4\right)} \times \frac{10}{5} = \textcolor{red}{5} \textcolor{b l u e}{\left(v + 4\right)} \times \frac{3 v + 10}{v + 4}$

$\cancel{\textcolor{red}{5}} \textcolor{b l u e}{\left(v + 4\right)} \times \frac{10}{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}}} = \textcolor{red}{5} \textcolor{b l u e}{\cancel{\left(v + 4\right)}} \times \frac{3 v + 10}{\textcolor{b l u e}{\cancel{\textcolor{b l a c k}{\left(v + 4\right)}}}}$

$10 \left(v + 4\right) = 5 \left(3 v + 10\right)$

Next, expand the terms in parenthesis:

$\left(10 \times v\right) + \left(10 \times 4\right) = \left(5 \times 3 v\right) + \left(5 \times 10\right)$

$10 v + 40 = 15 v + 50$

Then, subtract $\textcolor{red}{10 v}$ and $\textcolor{b l u e}{50}$ from each side of the equation to isolate the $v$ term while keeping the equation balanced:

$10 v - \textcolor{red}{10 v} + 40 - \textcolor{b l u e}{50} = 15 v - \textcolor{red}{10 v} + 50 - \textcolor{b l u e}{50}$

$0 - 10 = 5 v + 0$

$- 10 = 5 v$

Now, divide each side of the equation by $\textcolor{red}{5}$ to solve for $v$ while keeping the equation balanced:

$- \frac{10}{\textcolor{red}{5}} = \frac{5 v}{\textcolor{red}{5}}$

$- 2 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{5}}} v}{\cancel{\textcolor{red}{5}}}$

$- 2 = v$

$v = - 2$