Equation in a fraction - have I solved it right?

Question

I'm solving entrance maths example problems from a university. I solved this one:

$\frac {2x-3}5 - \frac {4x+5}3=8$

My solution was -104/14 but in the answer sheet it's -11. Am I wrong? If so why?

Edit: I did the following steps:

1. $3(2x-3)-5(4x+5)=8$
2. $6x-9-20x+25=120$
3. $-14x=104$
4. $x= -104/14$

Answer 1

You forgot parentheses around the numerator of the second fraction.

The calculations should look like: $$ \frac {2x-3}5 - \frac {4x+5}3=8\\ 6x-9-(20x+25)=120\\ 6x-9-20x-25=120\\ -14x-34=120\\ -14x=154\\ x=-11 $$

Answer 2

Look at $$3(2x-3)-5(4x+5)=120 \iff 6x - 9 - 20 x \color{blue}{- 25} = 120$$

$-5(4x+5) = -20 x-25$; you added +25 instead of subtracting 25.