How do you solve for t in $\frac{2}{7} (t + \frac{2}{3}) = \frac{1}{5} (t - \frac{2}{3})$ $2/7(t+2/3)=1/5(t-2/3)$ ?

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How do you solve for t in $\frac{2}{7} (t + \frac{2}{3}) = \frac{1}{5} (t - \frac{2}{3})$ $2/7(t+2/3)=1/5(t-2/3)$ ?

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Answer 1 · 2014-09-28T13:42:41

We can solve the question using the distributive property.

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

Multiplying , we get

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

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

Taking the like terms to one side of the equation;

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

Taking LCM,

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

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

$3 t = \frac{- 34 \cdot 35}{105}$ $3t = (-34*35 ) / 105$

$3 t = \frac{- 34 \cdot 1}{3}$ $3t = (-34 * 1 ) / 3$

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

$t = - \frac{34}{9} = - 3.7 7 or - 4$ $t = -34 /9 = -3.7 7 or -4$

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How do you solve for t in $\frac{2}{7} (t + \frac{2}{3}) = \frac{1}{5} (t - \frac{2}{3})$ $2/7(t+2/3)=1/5(t-2/3)$ ?

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