# How do you solve 3/4(4x+8)=-12 using the distributive property?

Jan 22, 2017

See the entire solution process below:

#### Explanation:

First, we distribute the $\textcolor{red}{\frac{3}{4}}$ term across each of the terms within the parenthesis:

$\left(\frac{\textcolor{red}{3}}{\textcolor{red}{4}} \times 4 x\right) + \left(\frac{\textcolor{red}{3}}{\textcolor{red}{4}} \times 8\right) = - 12$

$\left(\frac{\textcolor{red}{3}}{\cancel{\textcolor{red}{4}}} \times \textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x\right) + \left(\frac{\textcolor{red}{3}}{\cancel{\textcolor{red}{4}}} \times \textcolor{red}{\cancel{\textcolor{b l a c k}{8}}} 2\right) = - 12$

$3 x + 6 = - 12$

Next, subtract $\textcolor{red}{6}$ from each side of the equation to isolate the $x$ term while keeping the equation balanced:

$3 x + 6 - \textcolor{red}{6} = - 12 - \textcolor{red}{6}$

$3 x + 0 = - 18$

$3 x = - 18$

Now, divide each side of the equation by $\textcolor{red}{3}$ to solve for $x$ while keeping the equation balanced:

$\frac{3 x}{\textcolor{red}{3}} = - \frac{18}{\textcolor{red}{3}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{3}}} x}{\cancel{\textcolor{red}{3}}} = - 6$

$x = - 6$