# How do you solve 4 (2x - 1/2) = -6 (2/3x + 1/2)?

Jul 25, 2017

See a solution process below:

#### Explanation:

First, expand the terms in parenthesis on each side of the equation by multiplying each term within the parenthesis by the term outside the parenthesis:

$\textcolor{red}{4} \left(2 x - \frac{1}{2}\right) = \textcolor{b l u e}{- 6} \left(\frac{2}{3} x + \frac{1}{2}\right)$

$\left(\textcolor{red}{4} \cdot 2 x\right) - \left(\textcolor{red}{4} \cdot \frac{1}{2}\right) = \left(\textcolor{b l u e}{- 6} \cdot \frac{2}{3} x\right) + \left(\textcolor{b l u e}{- 6} \cdot \frac{1}{2}\right)$

$8 x - 2 = - \frac{12}{3} x + \left(- 3\right)$

$8 x - 2 = - 4 x - 3$

Next, add $\textcolor{red}{2}$ and $\textcolor{b l u e}{4 x}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$\textcolor{b l u e}{4 x} + 8 x - 2 + \textcolor{red}{2} = \textcolor{b l u e}{4 x} - 4 x - 3 + \textcolor{red}{2}$

$\left(\textcolor{b l u e}{4} + 8\right) x - 0 = 0 - 1$

$12 x = - 1$

Now, divide each side of the equation by $\textcolor{red}{12}$ to solve for $x$ while keeping the equation balanced:

$\frac{12 x}{\textcolor{red}{12}} = - \frac{1}{\textcolor{red}{12}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{12}}} x}{\cancel{\textcolor{red}{12}}} = - \frac{1}{12}$

$x = - \frac{1}{12}$