# How do you solve -4/15n + 2/3 = 2/5n?

Mar 12, 2018

$n = 1$

#### Explanation:

$- \frac{4}{15} \cdot n + \frac{2}{3} = \frac{2}{5} \cdot n$

$\left(\frac{2}{5} + \frac{4}{15}\right) \cdot n = \frac{2}{3}$

$\frac{2}{3} \cdot n = \frac{2}{3}$

$n = \frac{2}{3} \cdot \frac{3}{2}$

$n = 1$

Mar 12, 2018

$n = 1$

#### Explanation:

$- \frac{4}{15} n + \frac{2}{3} = \frac{2}{5} n \text{ } \leftarrow \times 15$ to get rid of the fractions

$- \frac{\cancel{15} \times 4}{\cancel{15}} n + \frac{{\cancel{15}}^{5} \times 2}{\cancel{3}} = \frac{{\cancel{15}}^{3} \times 2}{\cancel{5}} n$

$- 4 n + 10 = 6 n$

$- 6 n - 4 n = - 10$

$\text{ } - 10 n = - 10$

$\text{ } n = 1$