How do I solve this equation?

1. (5/2x) - (2/3) = (1/x) + (5/6)

*I will post what I did so far.

Question

How do I solve this equation? 

1. (5/2x) - (2/3) = (1/x) + (5/6)

*I will post what I did so far.

anonymous · Answer

is it $\frac{5}{2x}$ or $\frac{5}{2}x$ ?

anonymous · Answer

The first one.

anonymous · Answer

$$\frac{ 5 }{ 2x }$$ sorry for any confusion.

anonymous · Answer

$$\frac{ 15 - 4x}{ 6x } = \frac{ 6 + 5x }{ 6x }$$
Since they both have the same denominators, when you cross multiply, they will cancel out anyways so I then did:

15 - 4x = 6 + 5x
15 - 9x = 6
-9x = -10
$$x=\frac{ 10 }{ 9 }$$

I plugged the answer in for x and I did not get the same answer for the other side.

anonymous · Answer

i would add $\frac{2}{3}$ to both sides, subtract $\frac{1}{x}$ from both sides, and then cross multiply

anonymous · Answer

maybe that method would work as well, but $6-15=-9$ and not $-10$

anonymous · Answer

Whoops, well that's embarrassing :o lol. Thank you very much for your help!

anonymous · Answer

ye