# How do you solve: n + 2 = -14 - n?

Apr 4, 2017

See the entire solution process below:

#### Explanation:

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

$n + 2 - \textcolor{red}{2} + \textcolor{b l u e}{n} = - 14 - n - \textcolor{red}{2} + \textcolor{b l u e}{n}$

$n + \textcolor{b l u e}{n} + 2 - \textcolor{red}{2} = - 14 - \textcolor{red}{2} - n + \textcolor{b l u e}{n}$

$1 n + 1 \textcolor{b l u e}{n} + 0 = - 16 - 0$

$2 n = - 16$

Now, divide each side of the equation by $\textcolor{red}{2}$ to solve for $n$ while keeping the equation balanced:

$\frac{2 n}{\textcolor{red}{2}} = - \frac{16}{\textcolor{red}{2}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} n}{\cancel{\textcolor{red}{2}}} = - 8$

$n = - 8$

Apr 4, 2017

$n = - 8$

#### Explanation:

To solve this equation, collect terms in n on the left side and numeric values on the right side.

$n + n + 2 = - 14 \cancel{- n} \cancel{+ n}$

$\Rightarrow 2 n + 2 = - 14$

subtract 2 from both sides.

$2 n \cancel{+ 2} \cancel{- 2} = - 14 - 2$

$\Rightarrow 2 n = - 16$

divide both sides by 2

$\frac{\cancel{2} n}{\cancel{2}} = \frac{- 16}{2}$

$\Rightarrow n = - 8$

$\textcolor{b l u e}{\text{As a check}}$

Substitute this value into the equation and if the left side equals the right side then it is the solution.

$\text{left side } = - 8 + 2 = - 6$

$\text{right side } = - 14 - \left(- 8\right) = - 14 + 8 = - 6$

$\Rightarrow n = - 8 \text{ is the solution}$

Apr 4, 2017

$n = - 8$

#### Explanation:

You need to get all the variables ($n$) on one side and all the numbers on the other.
You want to get to the answer: $n = \text{a value}$

In an equation, you have to do the SAME to BOTH sides, otherwise the sides will no longer be equal.

$n + 2 = - 14 - n \text{ } \leftarrow$ add $n$ to each side first

$n + 2 \textcolor{red}{+ n} = - 14 - n \textcolor{red}{+ n}$

$2 n + 2 = - 14 \text{ } \leftarrow$ subtract $2$ from from sides

$2 n + 2 \textcolor{b l u e}{- 2} = - 14 \textcolor{b l u e}{- 2}$

$2 n = - 16 \text{ } \leftarrow \div 2$ to isolate $n$

$\frac{2 n}{2} = \frac{- 16}{2}$

$n = - 8$

Note that $- n \textcolor{red}{+ n} = 0 \text{ " and " } + 2 \textcolor{b l u e}{- 2} = 0$

Apr 4, 2017

$n = \text{-} 8$

#### Explanation:

First add $n$ to both sides to eliminate it from the right side
$n + 2 \textcolor{g r e e n}{+ n} = \text{-} 14 \textcolor{red}{\cancel{\textcolor{b l a c k}{- n}} \cancel{\textcolor{g r e e n}{+ n}}}$
$2 n + 2 = \text{-} 14$

Then subtract $2$ from both sides to isolate the $n$ term on the left side
$2 n \textcolor{red}{\cancel{\textcolor{b l a c k}{+ 2}} \cancel{\textcolor{g r e e n}{- 2}}} = \text{-} 14 \textcolor{g r e e n}{- 2}$
$2 n = \text{-} 16$

Finally divide both sides by $2$ to isolate $n$
$\textcolor{g r e e n}{\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} \textcolor{b l a c k}{n}}{\textcolor{red}{\cancel{\textcolor{g r e e n}{2}}}}} = \textcolor{g r e e n}{\frac{\textcolor{b l a c k}{\text{-} 16}}{2}}$
$n = \text{-} 8$