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

Apr 2, 2017

See the entire solution process below:

#### Explanation:

First, expand the terms in parenthesis on each side of the equation:

$\left(2 \times x\right) + \left(2 \times 6\right) = \left(- 2 \times x\right) - \left(- 2 \times 4\right)$

$2 x + 12 = - 2 x - \left(- 8\right)$

$2 x + 12 = - 2 x + 8$

Next, subtract $\textcolor{red}{12}$ and add $\textcolor{b l u e}{2 x}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$2 x + 12 - \textcolor{red}{12} + \textcolor{b l u e}{2 x} = - 2 x + 8 - \textcolor{red}{12} + \textcolor{b l u e}{2 x}$

$2 x + \textcolor{b l u e}{2 x} + 12 - \textcolor{red}{12} = - 2 x + \textcolor{b l u e}{2 x} + 8 - \textcolor{red}{12}$

$\left(2 + \textcolor{b l u e}{2}\right) x + 0 = 0 - 4$

$4 x = - 4$

Now, divide each side of the equation by $\textcolor{red}{4}$ to solve for $x$ while keeping the equation balanced:

$\frac{4 x}{\textcolor{red}{4}} = - \frac{4}{\textcolor{red}{4}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{4}}} x}{\cancel{\textcolor{red}{4}}} = - 1$

$x = - 1$

Aug 6, 2018

$x = - 1$

#### Explanation:

Let's distribute the $2$ on the left, and the $- 2$ on the right to get

$2 x + 12 = - 2 x + 8$

Next, let's add $2 x$ to both sides to get

$4 x + 12 = 8$

Let's subtract $12$ from both sides to get

$4 x = - 4$

Lastly, we can divide both sides by $4$ to get

$x = - 1$