# How do you solve 4(5k+3)+3(-4k-4)=-48 using the distributive property?

Feb 16, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms within parenthesis by multiplying each term within the parenthesis by the term outside the parenthesis. Be careful to manage the signs of the individual terms correctly:

$\textcolor{red}{4} \left(5 k + 3\right) + \textcolor{b l u e}{3} \left(- 4 k - 4\right) = - 48$ becomes:

$\left(\textcolor{red}{4} \times 5 k\right) + \left(\textcolor{red}{4} \times 3\right) - \left(\textcolor{b l u e}{3} \times 4 k\right) - \left(\textcolor{b l u e}{3} \times 4\right) = - 48$

$20 k + 12 - 12 k - 12 = - 48$

Next, group and combine like terms on the left side of the equation:

$20 k - 12 k + 12 - 12 = - 48$

$\left(20 - 12\right) k + 0 = - 48$

$8 k = - 48$

Now, divide each side of the equation by $\textcolor{red}{8}$ to solve for $k$ while keeping the equation balanced:

$\frac{8 k}{\textcolor{red}{8}} = - \frac{48}{\textcolor{red}{8}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} k}{\cancel{\textcolor{red}{8}}} = - 6$

$k = - 6$