# How do you solve -77=n-4(3-3n) using the distributive property?

Aug 9, 2017

$n = - 5$
(see below for application of distributive property)

#### Explanation:

Using the distributive property (in general):
$\textcolor{w h i t e}{\text{XXX}} \textcolor{red}{a} \left(b + c\right) = \left(\textcolor{red}{a} b + \textcolor{red}{a} c\right)$
and
$\textcolor{w h i t e}{\text{XXX}} \left(d + e\right) \textcolor{b l u e}{f} = \left(\mathrm{dc} o l \mathmr{and} \left(b l u e\right) f + e \textcolor{b l u e}{f}\right)$

Given
$- 77 = n - \textcolor{red}{4} \left(3 - 3 n\right)$
$\textcolor{w h i t e}{- 77} = n - \left(\textcolor{red}{4} \times 3 - \textcolor{red}{4} \times 3 n\right) \textcolor{w h i t e}{\text{xxxx}}$[distributive property]
$\textcolor{w h i t e}{- 77} = n - \left(12 - 12 n\right)$
$\textcolor{w h i t e}{- 77} = n - 12 + 12 n$
$\textcolor{w h i t e}{- 77} = 13 n - 12$
...adding $12$ to both sides:
$- 65 = 13 n$
...dividing both sides by $13$
$- 5 = n \textcolor{w h i t e}{\text{xxx")"or"color(white)("xxx}} n = - 5$