# How do you solve 2/3x-1/6=1/2x+5/6?

$\textcolor{red}{x = 6}$

#### Explanation:

Start from the given equation

$\frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6}$

We will use 6 on both sides of the equation to get rid of the fractions

Multiply both sides by 6

$6 \left(\frac{2}{3} x - \frac{1}{6}\right) = 6 \left(\frac{1}{2} x + \frac{5}{6}\right)$

$\frac{12 x}{3} - \frac{6}{6} = \frac{6 x}{2} + \frac{30}{6}$

Simplify

$4 x - 1 = 3 x + 5$

$4 x - 3 x = 5 + 1$

$\textcolor{red}{x = 6}$

Checking the answer $x = 6$ into the original equation

$\frac{2}{3} x - \frac{1}{6} = \frac{1}{2} x + \frac{5}{6}$

$\frac{2}{3} \left(6\right) - \frac{1}{6} = \frac{1}{2} \left(6\right) + \frac{5}{6}$

$\frac{12}{3} - \frac{1}{6} = \frac{6}{2} + \frac{5}{6}$

$\frac{23}{6} = \frac{23}{6}$

correct!

God bless....I hope the explanation is useful.