# How do you solve for t in 2/7(t+2/3)=1/5(t-2/3)?

Sep 28, 2014

We can solve the question using the distributive property.

$\frac{2}{7} \left(t + \frac{2}{3}\right) = \frac{1}{5} \left(t - \frac{2}{3}\right)$

Multiplying , we get

$\left(\frac{2}{7}\right) \cdot t + \left(\frac{2}{7}\right) \cdot \left(\frac{2}{3}\right) = \left(\frac{1}{5}\right) \cdot t - \left(\frac{1}{5}\right) \cdot \left(\frac{2}{3}\right)$

$\frac{2 t}{7} + \frac{4}{21} = \frac{t}{5} - \frac{2}{15}$

Taking the like terms to one side of the equation;

$\frac{2 t}{7} - \frac{t}{5} = - \frac{2}{15} - \frac{4}{21}$

Taking LCM,

$\frac{10 t - 7 t}{35} = \frac{\left(- 2 \cdot 7\right) + \left(- 4 \cdot 5\right)}{105}$

$\frac{3 t}{35} = - \frac{34}{105}$

$3 t = \frac{- 34 \cdot 35}{105}$

$3 t = \frac{- 34 \cdot 1}{3}$

$3 t = - \frac{34}{3}$

$t = - \frac{34}{9} = - 3.7 7 \mathmr{and} - 4$