# How do you solve -8( - 2- 5n ) - ( - 6n + 2) = 14?

Jan 12, 2018

$n = 0$

#### Explanation:

1) Multiply into the brackets.
$- 8 \left(- 2 - 5 n\right) - \left(- 6 n + 2\right) = 16 + 40 n + 6 n - 2 = 14$

2) Combine like terms
$16 + 40 n + 6 n - 2 = 46 n + 14 = 14$

Solve using opposite operations
$46 n + 14 = 14$

$46 n + 14 - \textcolor{red}{14} = 14 - \textcolor{red}{14}$

$46 n = 0$

$\frac{46 n}{\textcolor{red}{46}} = \frac{0}{\textcolor{red}{46}}$

$n = 0$

Jan 12, 2018

$n = 0$

#### Explanation:

$- 8 \left(- 2 - 5 n\right) - \left(- 6 n + 2\right) = 14$

$16 + 40 n + 6 n - 2 = 14$

Combine like-terms

$46 n + 14 = 14$

$46 n = 0$

$n = \frac{0}{46} = 0$

Jan 12, 2018

$n = 0$

#### Explanation:

$\text{distribute the brackets on left side of equation}$

$16 + 40 n + 6 n - 2 = 14$

$\Rightarrow 46 n + 14 = 14$

$\text{subtract 14 from both sides}$

$46 n \cancel{+ 14} \cancel{- 14} = 14 - 14$

$\Rightarrow 46 n = 0 \Rightarrow n = 0$

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

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

$- 8 \left(- 2\right) - \left(+ 2\right) = 16 - 2 = 14$

$\Rightarrow n = 0 \text{ is the solution}$