# How do you solve -6(n-5)=66 using the distributive property?

Aug 24, 2016

n = - 6

#### Explanation:

The $\textcolor{b l u e}{\text{distributive property}}$ means multiply the terms inside the bracket by the number outside the bracket.

In general, this is $\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{a \left(b + c\right) = a b + a c} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

So: $- 6 \left(n - 5\right) = 66 \Rightarrow \left(- 6 \times n\right) + \left(- 6 \times - 5\right) = 66$

$\Rightarrow - 6 n + 30 = 66$

subtract 30 from both sides of the equation.

$\Rightarrow - 6 n + \cancel{30} - \cancel{30} = 66 - 30 \Rightarrow - 6 n = 36$

now divide both sides by -6 to obtain n

$\frac{{\cancel{- 6}}^{1} n}{\cancel{- 6}} ^ 1 = {\cancel{36}}^{-} \frac{6}{\cancel{- 6}} ^ 1 \Rightarrow n = - 6$