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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. $x= -104/14$
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    $\begingroup$ Please show your working so that we can help you $\endgroup$ – Shuri2060 Jul 1 '17 at 16:53
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    $\begingroup$ Yes, you're wrong. If we are to have any chance of answering why, you have to show us your work. $\endgroup$ – Henrik Jul 1 '17 at 16:57
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    $\begingroup$ Note that you can simply plug your answer versus the given one into the equation to check if your answer is right. $\endgroup$ – Epiousios Jul 1 '17 at 17:09
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    $\begingroup$ The $8$ on the right in step $1$ should be $120$. You fix that in the next line, so no lasting harm. $\endgroup$ – Ross Millikan Jul 1 '17 at 21:41
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    $\begingroup$ You can easily debug such equational proofs using the methods described here. In your case since you know the solution you can plug in $\,x = -11$ to find the first equation that is false, which will reveal your first error. $\endgroup$ – Bill Dubuque Jul 2 '17 at 2:13
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You forgot parentheses around the numerator of the second fraction.

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

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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.

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  • $\begingroup$ oh I got it, I thought they made mistake not me) $\endgroup$ – Steve Jul 1 '17 at 17:09
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    $\begingroup$ It happens; everyone of us makes such errors on occasion! Thanks for the edit with the added work, btw! $\endgroup$ – Namaste Jul 1 '17 at 17:12
  • $\begingroup$ yeah, I just lack practice. Thanks for you, not me)) $\endgroup$ – Steve Jul 1 '17 at 17:16

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