How do you solve for r: r = 3p - 5r?

Mar 6, 2016

$r = \frac{p}{2}$

Explanation:

Given:$\text{ } \textcolor{b r o w n}{r = 3 p - 5 r}$

$\textcolor{b l u e}{\text{Method}}$

Collect and manipulate the terms until you have just one $r$ on the right hand side of the equals and everything on the other side.

$\textcolor{b l u e}{\text{Solving your question}}$

$\textcolor{g r e e n}{\text{Collecting terms}}$

Add $\textcolor{b l u e}{5 r}$ to both sides

$\textcolor{b r o w n}{r \textcolor{b l u e}{+ 5 r} = 3 p - 5 r \textcolor{b l u e}{+ 5 r}}$

$6 r = 3 p + 0$

$\textcolor{g r e e n}{\text{Manipulating so that there is only one } r}$

Divide both sides by $\textcolor{b l u e}{6}$

$\textcolor{b r o w n}{\frac{6}{\textcolor{b l u e}{6}} r = \frac{3}{\textcolor{b l u e}{6}} p}$

But $\frac{6}{6} = 1 \text{ and } \frac{3}{6} = \frac{1}{2}$

$r = \frac{p}{2}$