# Question #71169

Mar 7, 2017

See the entire solution process and answer below:

#### Explanation:

First, expand the terms within parenthesis on the left side of the equation by multiplying each term within the parenthesis by $\textcolor{red}{4}$ which is the term outside the parenthesis:

$6 + \left(\textcolor{red}{4} \times r\right) - \left(\textcolor{red}{4} \times 2\right) = r + 7$

$6 + 4 r - 8 = r + 7$

$6 - 8 + 4 r = r + 7$

$- 2 + 4 r = r + 7$

Next, add $\textcolor{red}{2}$ and subtract $\textcolor{b l u e}{r}$ from each side of the equation to isolate the $r$ term while keeping the equation balanced:

$- 2 + 4 r + \textcolor{red}{2} - \textcolor{b l u e}{r} = r + 7 + \textcolor{red}{2} - \textcolor{b l u e}{r}$

$- 2 + \textcolor{red}{2} + 4 r - \textcolor{b l u e}{r} = r - \textcolor{b l u e}{r} + 7 + \textcolor{red}{2}$

$0 + 3 r = 0 + 9$

$3 r = 9$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $r$ while keeping the equation balanced:

$\frac{3 r}{\textcolor{red}{3}} = \frac{9}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} r}{\cancel{\textcolor{red}{3}}} = 3$

$r = 3$