# What is the value of x in the equation 2/3(1/2x+12)=1/2(1/3x+14)-3?

Jan 12, 2017

$x = - 24$

#### Explanation:

We start with $\frac{2}{3} \left(\frac{1}{2} x + 12\right) = \frac{1}{2} \left(\frac{1}{3} x + 14\right) - 3$.

The first thing we do is distribute the $\frac{2}{3}$ and $\frac{1}{2}$.

That gives us $\frac{2}{6} x + 8 = \frac{1}{6} x + 7 - 3$.

If we simplify the equation, we get $\frac{2}{6} x + 8 = \frac{1}{6} x + 4$.

Now we just subtract $\frac{1}{6} x$ on both sides and subtract $8$.

$\frac{2}{6} x - \frac{1}{6} x = 4 - 8$ or $\frac{1}{6} x = - 4$.

Just multiply both sides by $6$ and we find $x$.

$\cancel{\textcolor{b l u e}{6}} \cdot \frac{1}{\cancel{6}} x = - 4 \cdot \textcolor{b l u e}{6}$ or $\textcolor{red}{x = - 24}$.

Just to make sure we're right, let's plug $- 24$ in for $x$ and solve.

$\frac{2}{3} \left(\frac{1}{2} \cdot \textcolor{red}{- 24} + 12\right) = \frac{1}{2} \left(\frac{1}{3} \cdot \textcolor{red}{- 24} + 14\right) - 3$

$\frac{2}{3} \left(- 12 + 12\right) = \frac{1}{2} \left(- 8 + 14\right) - 3$

$0 = \frac{1}{2} \cdot 6 - 3$

$0 = 3 - 3$

$0 = 0$

We were right! $x = - 24$