# How do you solve 1/3x + 2 = 1/6x + 11/2?

Sep 6, 2016

$x = 21$

#### Explanation:

$\frac{1}{3} x + 2 = \frac{1}{6} x + \frac{11}{2}$

or

$\frac{1}{3} x - \frac{1}{6} x = \frac{11}{2} - 2$

or

$\frac{1}{6} x = \frac{7}{2}$

or

$x = \frac{7}{2} \times 6$

or

$x = 21$

Sep 6, 2016

The same thing but in disguise

$x = 21$

#### Explanation:

Lets get rid of the fractions.

Make all the denominators 6

$\frac{2}{6} x + \frac{12}{6} = \frac{1}{6} x + \frac{33}{6}$

Now totally disregard the denominators

$2 x + 12 = x + 33$

$2 x - x = 33 - 12$

$x = 21$

Sep 6, 2016

$x = 21$

#### Explanation:

If you have an equation which has fractions, you can get rid of the fractions by

"multiply through by the LCD"

This allows you to cancel all the denominators, which makes the entire equation simpler.

$\textcolor{w h i t e}{\times \times \times x} \frac{1}{3} x + 2 = \frac{1}{6} x + \frac{11}{2} \textcolor{w h i t e}{\times \times \times \times x} \leftarrow L C D = 6$

$\frac{\textcolor{red}{{\cancel{6}}^{2} \times} 1}{\cancel{3}} x + \textcolor{red}{6 \times} 2 = \frac{\textcolor{red}{\cancel{6} \times} 1}{\cancel{6}} x + \frac{\textcolor{red}{{\cancel{6}}^{3} \times} 11}{\cancel{2}}$

$\textcolor{w h i t e}{\times x . \times x} 2 x + 12 = x + 33$

$\textcolor{w h i t e}{\times \times \times \times \times x} x = 21$