# How do you solve \frac { v } { 5} + \frac { 2} { 3} = \frac { 6} { 5} + \frac { v } { 15}?

Mar 20, 2018

$v = 4$

#### Explanation:

$\setminus \frac{v}{5} + \setminus \frac{2}{3} = \setminus \frac{6}{5} + \setminus \frac{v}{15}$

Take the terms with variable $v$ on left hand side and keep rest on Right hand side:

$\setminus \frac{v}{5} - \setminus \frac{v}{15} = \setminus \frac{6}{5} - \setminus \frac{2}{3}$

Make the denominators equal:

$\implies \setminus \frac{v}{5} \times \frac{3}{3} - \setminus \frac{v}{15} = \setminus \frac{6}{5} \times \frac{3}{3} - \setminus \frac{2}{3} \times \frac{5}{5}$

$\implies \setminus \frac{3 v}{15} - \setminus \frac{v}{15} = \setminus \frac{18}{15} - \setminus \frac{10}{15}$

$\implies \setminus \frac{3 v - v}{15} = \setminus \frac{18 - 10}{15}$

$\implies \frac{2 v}{15} = \frac{8}{15}$

$\implies 2 v = \frac{8}{15} \times 15$

$\implies 2 v = 8$

$\implies v = \frac{8}{2} = 4$

$\therefore v = 4$