# How do you solve -5( 1- v ) = 2( 1+ 2v )?

Mar 4, 2018

See a solution process below:

#### Explanation:

First, expand the terms on each side of the equation by multiiplying each of the terms within parenthesis by the term outside the parenthesis:

$\textcolor{red}{- 5} \left(1 - v\right) = \textcolor{b l u e}{2} \left(1 + 2 v\right)$

$\left(\textcolor{red}{- 5} \times 1\right) - \left(\textcolor{red}{- 5} \times v\right) = \left(\textcolor{b l u e}{2} \times 1\right) + \left(\textcolor{b l u e}{2} \times 2 v\right)$

$- 5 - \left(- 5 v\right) = 2 + 4 v$

$- 5 + 5 v = 2 + 4 v$

Now, add $\textcolor{red}{5}$ and subtract $\textcolor{b l u e}{4 v}$ from each side of the equation to solve for $v$ while keeping the equation balanced:

$- 5 + \textcolor{red}{5} + 5 v - \textcolor{b l u e}{4 v} = 2 + \textcolor{red}{5} + 4 v - \textcolor{b l u e}{4 v}$

$0 + \left(5 - \textcolor{b l u e}{4}\right) v = 7 + 0$

$1 v = 7$

$v = 7$