Jun 27, 2017

$x = \frac{32}{7}$

#### Explanation:

The first step is to multiply the $\frac{1}{2}$ term through the $\left(x - 6\right)$ term.

$\frac{1}{2} x - \frac{1}{2} \left(6\right) + \frac{1}{4} \left(x - 12\right) = 2 - x$

Because one half of six is three, we can rewrite it as

$\frac{1}{2} x - 3 + \frac{1}{4} \left(x - 12\right) = 2 - x$

Next, multiply the $\frac{1}{4}$ term through the $\left(x - 12\right)$ term.

$\frac{1}{2} x - 3 + \frac{1}{4} x - \frac{1}{4} \left(12\right) = 2 - x$

Because one quarter of 12 is 3, we can rewrite it as

$\frac{1}{2} x - 3 + \frac{1}{4} x - 3 = 2 - x$

You can combine the $\frac{1}{2} x$ and the $\frac{1}{4} x$. Because

$\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$, we can rewrite our equation as

$\frac{3}{4} x - 3 - 3 = 2 - x$

Because negative 3 minus 3 is negative six, we can rewrite

$\frac{3}{4} x - 6 = 2 - x$

Add $6$ to both sides

$\frac{3}{4} x = 8 - x$

Add $x$ to both sides

$\frac{3}{4} x + x = 8$

Because $x$ is really just $1 \times x$, we can rewrite as

$\frac{3}{4} x + 1 \times x = 8$

$\frac{3}{4} x + \frac{4}{4} x = 8$

$\frac{7}{4} x = 8$

Multiply both sides by $4$

$7 x = 32$

Divide both sides by 7

$x = \frac{32}{7}$