# How do you solve 3n + 15= 4- n - 3?

Jun 12, 2017

See a solution process below:

#### Explanation:

First, combine like terms on the left side of the equation:

$3 n + 15 = 4 - 3 - n$

$3 n + 15 = 1 - n$

Next, subtract $\textcolor{red}{15}$ and add $\textcolor{b l u e}{n}$ to each side of the equation to isolate the $n$ term while keeping the equation balanced:

$3 n + 15 - \textcolor{red}{15} + \textcolor{b l u e}{n} = 1 - n - \textcolor{red}{15} + \textcolor{b l u e}{n}$

$3 n + \textcolor{b l u e}{n} + 15 - \textcolor{red}{15} = 1 - \textcolor{red}{15} - n + \textcolor{b l u e}{n}$

$3 n + \textcolor{b l u e}{1 n} + 0 = - 14 - 0$

$\left(3 + \textcolor{b l u e}{1}\right) n = - 14$

$4 n = - 14$

Now, divide each side of the equation by $\textcolor{red}{4}$ to solve for $n$ while keeping the equation balanced:

$\frac{4 n}{\textcolor{red}{4}} = - \frac{14}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} n}{\cancel{\textcolor{red}{4}}} = - \frac{2 \times 7}{\textcolor{red}{2 \times 2}}$

$n = - \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \times 7}{\textcolor{red}{\textcolor{b l a c k}{\cancel{\textcolor{red}{2}}} \times 2}}$

$n = - \frac{7}{2}$