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Solving for x in this equation

  1. Feb 8, 2010 #1
    I'm not sure it is the correct thread, but it did say Algebra homeworks could be posted here too right? :biggrin:

    1. The problem statement, all variables and given/known data

    3bx - ab + 2a^2 = 2ax + 3b^2

    solve for the x.

    2. Relevant equations

    none


    3. The attempt at a solution

    3bx - ab + 2a^2 = 2ax + 3b^2
    2a^2 - 3b^2 = 2ax - 3bx + ab
    2a^2 - 3b^2 = x(2a - 3b) + ab
    2a^2 - 3b^2 -ab = x(2a - 3b)

    after which, I'm, stuck :confused:I don't know what to do anymore, nor do I know if I'm dog it right! my book says, the answer should be x=a+b. sadly, it doesn't give an explanation as to how it got the answer :cry:please help? I really need to pass my exam two days from now, and solution sets is a big part of it.
     
    Last edited: Feb 8, 2010
  2. jcsd
  3. Feb 8, 2010 #2

    CompuChip

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    You could try writing the left hand side as (2a - 3b) ( ... ) and divide out (2a - 3b) (provided it is not zero).
     
  4. Feb 8, 2010 #3
    First, put the terms with x on one side and the rest on the other side.Then, factor x out and divide both sides to have the x alone on one side.Finally,simplify.
     
  5. Feb 8, 2010 #4
    I can understand your struggle when you have the answer but you dont know how they get there, anyway I have much simpler way to do it .. you reached to a good step .. so all what left is to perform a division.. I made a figure illustrating the idea .. just go with me step by step :


    http://img189.imageshack.us/img189/9431/11291260.jpg [Broken]

    as you can see it is just a long division but this time it is with two variables .. so how to do it?

    well,

    first : take a as your variable and anything else as constant (check the red colored writing) divide 2a with 2a^2 put the result up (which is a ) then multiply it with 2a - 3b and write it below 2a^2 - 3b^2-ab (each result below the one that looks similar to it)

    second : take b as your variable and anything else as constant (check the blue colored writing) divide -3b with -3b^2 and put the result up (which is b) then multiply it with 2a - 3b and write the result below 2a^2 - 3b^2 -ab ( also put each result below the one that looks similar to it)

    thired : change the sign of all the previous results (check the green colored writing) and add every thing , you will end up with zero with tells you that when you divide 2a^2 - 3b^2 -ab with 2a-3b that will give you a+b with no reminder ..

    I hope now you got it :) .. and good luck with your test ..
     
    Last edited by a moderator: May 4, 2017
  6. Feb 8, 2010 #5

    ehild

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    Gold Member

    You can rewrite the left side as

    2a^2-2b^2 -b^2-ab= 2(a^2-b^2)-b(b+a)=
    =2(a-b)(a+b)-b(a+b)= (a+b)(2a-2b-b)=(a+b)(2a-3b)

    So the equation becomes: (a+b)(2a-3b)=x(2a-3b)

    Divide both sides by 2a-3b (supposing it is not 0) the result is x=a+b.
    If 2a-3b=0 any x is solution.

    ehild
     
  7. Feb 8, 2010 #6

    CompuChip

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    So, the four of us have now provided you with the complete answer :)
     
  8. Feb 14, 2010 #7
    ohmy :) thank you thank you thank you! I'm glad all of you have responded :redface:
     
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