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A+2b=2a+b=>1=2. please tell me what is the problem

  1. Jan 6, 2012 #1
    if we get:

    a+2b=2a+b
    =>a-b=2a-2b
    =>a-b=2(a-b)
    =>1=2

    I can't figure out the problem in it..please tell me
     
  2. jcsd
  3. Jan 6, 2012 #2
    Does 2*0=3*0 also imply 2=3??
     
  4. Jan 6, 2012 #3

    HallsofIvy

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    Science Advisor

    So 2b- b= 2a- a which gives a= b.

    Since a= b, a- b= 0 and you cannot divide by 0.0

     
  5. Jan 6, 2012 #4
    Note that the law

    [tex]ax=bx~\Rightarrow~a=b[/tex]

    Only holds if x is nonzero!!

    The correct way in solving this is

    [tex]ax=bx~\Rightarrow~ ax-bx=0~\Rightarrow~(a-b)x=0~\Rightarrow ~a-b=0~\text{or}~x=0[/tex]
     
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