The method to solving this problem is to isolate x first by adding `3/2` on both sides.

`5/12-5/6=x-3/2` `=> 5/12-5/6+3/2 = x`

Then, in order to evaluate fractions that have a different denominator (value on the bottom of the fraction bar), we must find the denominators' lowest common multiple, which in this case is 12.

`5/12-5/6+3/2 = x => 5/12-5/6*2/2+3/2*6/6 = x`

We can do these multiplications because it is essentially multiplying by 1 and does not change the values in the equation. The above equation becomes:

`5/12-10/12+18/12 = x` which simplifies to `13/12 = x`

**Therefore, `x = 13/12` **

The equation 5/12-5/6=x-3/2 has to be solved for x.

5/12-5/6=x-3/2

=> x = 5/12 - 5/6 + 3/2

=> x = 13/12

**The solution of the equation 5/12-5/6=x-3/2 is x = 13/12**