# How do you solve -4(2/3) = (2n/3) + (1/2) + (n/3)?

Jun 12, 2015

$n = - \frac{19}{3}$

#### Explanation:

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

$- \frac{8}{3} = \frac{2 n}{3} + \frac{1}{2} + \frac{n}{3}$ =

Subtract $\frac{1}{2}$ from both sides.

$- \frac{1}{2} - \frac{8}{3} = \frac{\cancel{3} n}{\cancel{3}}$ =

$- \frac{1}{2} - \frac{8}{3} = n$

The common denominator for $- \frac{1}{2} \mathmr{and} - \frac{8}{3}$ is $6$.

$- \frac{1}{2} \cdot \left(\frac{3}{3}\right) - \frac{8}{3} \cdot \left(\frac{2}{2}\right) = n$ =

$- \frac{3}{6} - \frac{16}{3} = n$ =

$- \frac{19}{3} = n$

Switch sides.

$n = - \frac{19}{3}$