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

Apr 11, 2017

See the entire solution process below:

#### Explanation:

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

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

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

$2 x - 2 + 3 = x - 3 x - 3$

$2 x + 1 = - 2 x - 3$

Next, subtract $\textcolor{red}{1}$ 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:

$\textcolor{b l u e}{2 x} + 2 x + 1 - \textcolor{red}{1} = \textcolor{b l u e}{2 x} - 2 x - 3 - \textcolor{red}{1}$

$4 x + 0 = 0 - 4$

$4 x = - 4$

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

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

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

$x = - 1$