# How do you solve 7/15x+5/6=2/3x+3/5?

Apr 11, 2018

$x = \frac{7}{6}$

#### Explanation:

move the $x$ values on one side, and the numbers on the other side

$\frac{7}{15} x + \frac{5}{6} = \frac{2}{3} x + \frac{3}{5}$

$\frac{7}{15} x - \frac{2}{3} x$ = $\frac{3}{5} - \frac{5}{6}$

$- \frac{1}{5} x = - \frac{7}{30}$

$x = - \frac{7}{30} \div - \frac{1}{5}$

$x = \frac{7}{6}$

Apr 11, 2018

$\frac{7}{6}$

#### Explanation:

$\frac{7}{15} + \frac{5}{6} = \frac{2}{3} x + \frac{3}{5}$

multiply both sides by $30$

$\therefore 14 x + 25 = 20 x + 18$

$\therefore 14 x - 20 x = 18 - 25$

$\therefore - 6 x = - 7$

multiply both sides by $- 1$

$\therefore 6 x = 7$

$\therefore x = \frac{7}{6}$
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check:-

substitute $x = \frac{7}{6}$

$\therefore \frac{7}{15} \left(\frac{7}{6}\right) + \frac{5}{6} = \frac{2}{3} \left(\frac{7}{6}\right) + \frac{3}{5}$

$\therefore \frac{49}{90} + \frac{5}{6} = \frac{7}{9} + \frac{3}{5}$

multiply both sides by $90$

$\therefore 49 + 75 = 70 + 54$

$\therefore 124 = 124$