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How do you find the solution set for $\frac{2}{3} a - \frac{1}{5} a = 2$ $2/3a - 1/5a = 2$ ?

1 Answer

Aug 15, 2015

If you multiply both sides by $15$ $15$ you can clear the denominators and solve as a simple integer equation to get:
$XXXX$ $color(white)("XXXX")$ $a = \frac{30}{7} = 4 \frac{2}{7}$ $a= 30/7 = 4 2/7$

Explanation:

Given $\frac{2}{3} a - \frac{1}{5} a = 2$ $2/3a-1/5a=2$

Multiply both sides by $15$ $15$
$XXXX$ $color(white)("XXXX")$ $10 a - 3 a = 30$ $10a - 3a = 30$
Simplify the left side
$XXXX$ $color(white)("XXXX")$ $7 a = 30$ $7a = 30$
Divide both sides by $7$ $7$
$XXXX$ $color(white)("XXXX")$ #a = 30/7

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