# How do you simplify 4x-2+(-6x)+8?

Jan 21, 2017

See a solution process below for: 4x + 2 = 6x - 8

#### Explanation:

First, subtract $\textcolor{red}{4 x}$ and add $\textcolor{b l u e}{8}$ to each side of the equation to isolate the $x$ term while keeping the equation balanced:

$4 x - \textcolor{red}{4 x} + 2 + \textcolor{b l u e}{8} = 6 x - \textcolor{red}{4 x} - 8 + \textcolor{b l u e}{8}$

$0 + 10 = \left(6 - \textcolor{red}{4}\right) x - 0$

$10 = 2 x$

Now, divide each side of the fraction by $\textcolor{red}{2}$ to solve for $x$ while keeping the equation balanced:

$\frac{10}{\textcolor{red}{2}} = \frac{2 x}{\textcolor{red}{2}}$

$5 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}} x}{\cancel{\textcolor{red}{2}}}$

$5 = x$

$x = 5$

Jan 21, 2017

$4 x - 2 + \left(- 6 x\right) + 8 = - 2 x + 6$

#### Explanation:

First, since $4 x - 2 = 4 x + \left(- 2\right)$

We can say

$4 x - 2 + \left(- 6 x\right) + 8 = 4 x + \left(- 2\right) + \left(- 6 x\right) + 8$

Then we group like terms

$4 x + \left(- 6 x\right) + \left(- 2\right) + 8 = \left(4 x + \left(- 6 x\right)\right) + \left(\left(- 2\right) + 8\right)$

Then we simplify

$= \left(4 x - 6 x\right) + \left(8 - 2\right) = \left(- 2 x\right) + \left(6\right) = \underline{- 2 x + 6}$