# How do you solve for r in S=L(1-r)?

Mar 13, 2018

See a solution process below:

#### Explanation:

First, divide each side of the equation by $\textcolor{red}{L}$ to eliminate the need for parenthesis while keeping the equation balanced:

$\frac{S}{\textcolor{red}{L}} = \frac{L \left(1 - r\right)}{\textcolor{red}{L}}$

$\frac{S}{L} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{L}}} \left(1 - r\right)}{\cancel{\textcolor{red}{L}}}$

$\frac{S}{L} = 1 - r$

Next subtract $\textcolor{red}{\frac{S}{L}}$ and add $\textcolor{b l u e}{r}$ to each side of the equation to solve for $r$ while keeping the equation balanced:

$\frac{S}{L} - \textcolor{red}{\frac{S}{L}} + \textcolor{b l u e}{r} = 1 - \textcolor{red}{\frac{S}{L}} - r + \textcolor{b l u e}{r}$

$0 + r = 1 - \frac{S}{L} - 0$

$r = 1 - \frac{S}{L}$

Or

$r = \frac{L}{L} - \frac{S}{L}$

$r = \frac{L - S}{L}$