# How do you solve 4x - 2 = 2x + 8?

Oct 22, 2016

$x = 5$

#### Explanation:

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

Bring like terms to one side:

$4 x - 2 x = 8 + 2$

$2 x = 10$

Divide both sides by $2$:

$x = 5$

Oct 22, 2016

$x = 5$

#### Explanation:

$4 x - 2 = 2 x + 8$

We eleminate 2x on the right by substracting 2x from each side.
Equivalently, we can add -2x to both sides.
$4 x - 2 \textcolor{red}{- 2 x} = 2 x \textcolor{red}{- 2 x} + 8$

Simplify
$2 x - 2 = 8$

Add 2 to each side.
$2 x - 2 \textcolor{red}{+ 2} = 8 \textcolor{red}{+ 2}$

$2 x = 10$

Multiply each side by 1/2
2x color(red)(xx(1/2)) = 10 color(red)(xx 1/2

$x = 5$

Check !

$4 x - 2 = 2 x + 8$ substitute x=5 into equation

$4 \left(5\right) - 2 = 2 \left(5\right) + 8$
$20 - 2 = 10 + 8$
$18 = 18$