# 3/4=x-3/5x?

Mar 9, 2018

$x = \frac{15}{8}$

#### Explanation:

$\frac{3}{4} = x - \frac{3}{5} x$

Sometimes it helps to rewrite the problem, I see an invisible 1 in there that may make things easier to think about if I write it in...

$\frac{3}{4} = \left(1 \cdot x\right) - \left(\frac{3}{5} \cdot x\right)$

Now I can clearly see that I have two numbers, 1 and $\frac{3}{5}$ being multiplied by $x$ and subtracted from each other. Since they are both being multiplied by $x$ we can factor that $x$ out and work with two constants which makes our lives easier, so lets do that :)

$\frac{3}{4} = x \cdot \left(1 - \frac{3}{5}\right) = x \cdot \left(\frac{5}{5} - \frac{3}{5}\right) = x \cdot \left(\frac{2}{5}\right)$

so,
$\frac{3}{4} = x \frac{2}{5}$

Finally I can multiply both sides by the reciprocal of $\frac{2}{5}$, $\frac{5}{2}$, to isolate x and solve the problem!

$\frac{3}{4} \cdot \frac{5}{2} = x \frac{2}{5} \cdot \frac{5}{2} = x = \frac{15}{8}$

So, $x = \frac{15}{8}$ :D