You're a programmer? Then you should understand even more how important parentheses are!
But you still refuse to use parentheses. "x- 4 over 2" could mean (x- 4)/2 or x- (4/2).
Also, originally, you had "x- 4/3" but now you say "x- 4 over [b]2[/sup]"!
In any case, if it were either x- (4/2) on the left or (x- 4)/2, the two sides can't be equal, the "x" would cancel on the left.
I suspect you mean (x- 5)/2- (x- 4)/3= (x- 3)/2- x- 2 but that is still not true! On the left, when you combine the fractions, you will have
but on the right
What you have written simply cannot be true.
Most programmers understand the GIGO principle (Garbage in, garbage out) ....
My advice to the OP is to get each side over a common denominator of 6, simplify the resulting numerators and then equate. You end up with x - 7 = -3x + 3 and solving for x is simple.
There is a huge difference (as example) between x - 5/2 and (x - 5)/2
100 - 20/5 = 100 - 4 = 96
(100 - 20)/5 = 80/5 = 16 ; do you "get it" now?
I too am surprised that you're a programmer and didn't know this.
More so since you stated this on one of your previous posts:
" I am not in school I haven't been for a while. I was attempting to help a friend got to this problem and its bugging me."
Can you answer this:
(x - 5)/2 * 6 = ?
If not, you need to learn the Algebra basics; can't "teach" that here, sorry.