Can someone please explain in detail so I understand how x-5/2 - x-4/3 = x-3/2 - (x-2)
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
$\displaystyle \frac{3x- 15}{6}- \frac{2x- 8}{6}= \frac{x- 7}{6}$
but on the right $\displaystyle \frac{x- 3}2- x- 2= \frac{x- 3}{2}- \frac{2x+ 2}{2}= -\frac{x- 5}{2}$
What you have written simply cannot be true.
It would appear that the question is meant to be:
Solve $\displaystyle \dfrac{x-5}{2} - \dfrac{x-4}{3} = \dfrac{x-3}{2} - (x-2)$.
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.
Next time, use BRACKETS in order to show properly: (x - 5)/2 - (x - 4)/3 = (x - 3)/2 - (x - 2)
There is a huge difference (as example) between x - 5/2 and (x - 5)/2
Take this:
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.