# How do you solve 15 + 6n = 7(2n + 3)?

Mar 7, 2017

See the entire solution process below:

#### Explanation:

First, expand the term within parenthesis on the right side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$15 + 6 n = 7 \left(2 n + 3\right)$

$15 + 6 n = \left(7 \times 2 n\right) + \left(7 \times 3\right)$

$15 + 6 n = 14 n + 21$

Next, subtract $\textcolor{red}{6 n}$ and $\textcolor{b l u e}{21}$ from each side of the equation to isolate the $n$ term while keeping the equation balanced:

$15 + 6 n - \textcolor{red}{6 n} - \textcolor{b l u e}{21} = 14 n + 21 - \textcolor{red}{6 n} - \textcolor{b l u e}{21}$

$15 - \textcolor{b l u e}{21} + 6 n - \textcolor{red}{6 n} = 14 n - \textcolor{red}{6 n} + 21 - \textcolor{b l u e}{21}$

$- 6 + 0 = 8 n + 0$

$- 6 = 8 n$

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

$- \frac{6}{\textcolor{red}{8}} = \frac{8 n}{\textcolor{red}{8}}$

$- \frac{6}{8} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} n}{\cancel{\textcolor{red}{8}}}$

$- \frac{2 \times 3}{2 \times 4} = n$

$- \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 3}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 4} = n$

$- \frac{3}{4} = n$

$n = - \frac{3}{4}$