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Homework Help: Solve this equation

  1. May 30, 2010 #1
    Can someone please tell me where I have gone wrong here? I have to solve the following equation:

    (3x - 7)/4 - (4x + 5)/2 = 3/4

    I attempted to do it by muliplying boths sides by 4 to get rid of the denominators, leaving me with:

    3x - 7 - 8x + 10 = 3
    simplified: -5x + 3 = 3

    which is clearly nonsense as that means -5x would equal 0.
     
  2. jcsd
  3. May 30, 2010 #2

    Cyosis

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    Homework Helper

    You have incorrectly distributed the minus 1 over the second term in brackets.
     
  4. May 30, 2010 #3
    Hi Cyosis. Thanks for your reply. I'm afraid I don't understand. can you clarify your statement please?
    Many thanks
     
  5. May 30, 2010 #4

    Cyosis

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    Sure, [tex]-(4x+5)=-4x-5 \neq \underbrace{-4x+5}_\text{what you did}[/tex].
     
  6. May 30, 2010 #5
    Besides what Cyosis said, there's another problem here...

    If you reach the conclusion that -5x = 0 in an arbitrary equation, there is nothing (necessarily) wrong with that. Just divide both sides by -5 and the result is that x = 0. "-5x = 0" is false for many values of x, but it is not ALWAYS false, as we have seen.

    If you reach a conclusion that is ALWAYS false (e.g. " 1=2 "), then that is nonsense.

    x = 0 would have been the solution, had you arrived at -5x = 0 in a correct way.
     
  7. May 31, 2010 #6
    If you put it on a commen dinominator

    like this [tex]\frac{(3x-7)-(8x+10)}{4} = \frac{3}{4}[/tex] and multiply both sides by 4 and clean up the act you get

    [tex]-5x -17 = 3 \Leftrightarrow -5x = 20 [/tex] and thus the only x which solves the original eqn is x = -4.
     
    Last edited: May 31, 2010
  8. May 31, 2010 #7

    Borek

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    Staff: Mentor

    No, you did exactly the same mistake Gringo did. -7-(+10) is not 3.
     
  9. May 31, 2010 #8
    Its gringa, jefe ;)

    and sorry its early here in my part of the Univers...
     
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