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Absolute value on both side of equation

  1. Aug 23, 2010 #1
    I solved this absolute value equation and I am confuse about the answer given in the book for this question, the answer in the book is x > = 0 or x = -2/3 please tell me how can I get this answer from the following solution. Please tell the method which should be true for all such type of questions.
    look at the image below
    [PLAIN]http://img261.imageshack.us/img261/1577/imgsb.jpg [Broken]
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Aug 23, 2010 #2
    ok well... one of the mistakes I see is how you reached the conclusion "3x +2 =3x +2 for all real nobs"

    well, this isn't true... is it? ex: x= -1. |3(-1)+2(-1)| does not equal (-1)|3(-1)+2|.

    Break it up like this:
    {[tex] |3x^2 + 2x|= |x||3x+2| = x |3x + 2| [/tex] } [tex] \Rightarrow [/tex] { [tex] |x|=x , for (3x+2) \neq 0 [/tex] }

    Hence, this is true for all [tex] x \geq 0[/tex].

    Now, separately consider the case (3x+2)=0. What do you get? x= -2/3

    Note: LaTeX is being crazy!
    Last edited: Aug 23, 2010
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