# How do you solve t- \frac { 5} { 8} t + \frac { 3} { 5} = \frac { 3} { 5} ( t + \frac { 5} { 2} )?

Nov 3, 2016

$t = - 4$

#### Explanation:

solve $t - \frac{5}{8} t + \frac{3}{5} = \frac{3}{5} \left(t + \frac{5}{2}\right)$
multiply everything by the LCD which is 40
$40 \left(t - \frac{5}{8} t + \frac{3}{5} = \frac{3}{5} \left(t + \frac{5}{2}\right)\right)$
$40 t - 25 t + 24 = 24 \left(t + \frac{5}{2}\right)$
simplify and distribute parenthesis
$15 t + 24 = 24 t + 60$
solve for t
$15 t - 24 t = 60 - 24$
$- 9 t = 36$
$t = - 4$