How do you solve 6=3(r+6)+5(r+4) using the distributive property?

1 Answer
Feb 6, 2017

See the entire solution process below:

Explanation:

First, expand the terms in parenthesis on the right side of the equation:

$6 = \left(3 \times r\right) + \left(3 \times 6\right) + \left(5 \times r\right) + \left(5 \times 4\right)$

$6 = 3 r + 18 + 5 r + 20$

Now, group and combine like terms on the right side of the equation:

$6 = 3 r + 5 r + 18 + 20$

$6 = \left(3 + 5\right) r + 38$

$6 = 8 r + 38$

Next, subtract $\textcolor{red}{38}$ from each side of the equation to isolate the $r$ term while keeping the equation balanced:

$6 - \textcolor{red}{38} = 8 r + 38 - \textcolor{red}{38}$

$- 32 = 8 r + 0$

$- 32 = 8 r$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $r$ while keeping the equation balanced:

$\frac{- 32}{\textcolor{red}{8}} = \frac{8 r}{\textcolor{red}{8}}$

$- 4 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} r}{\cancel{\textcolor{red}{8}}}$

$- 4 = r$

$r = - 4$