You said that n/3 = n/2 + 12 .
There's only one number that 'n' can be.
It may or may not be an integer. We'll have to see.
Subtract n/2 from each side: n/3 - n/2 = 12
Multiply each side by 12 : 4n - 6n = 144
Do the subtraction on the left: - 2n = 144
Divide each side by -2 : n = - 72
Yep. It turns out that 'n' is an integer.
It didn't have to be, just because you said so.
For example, if you said that n/3 is only
11 greater than n/2 , we could figure out
what number 'n' must be, and it wouldn't
be an integer.