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Homework Help: Proof of an expression involving absolute value

  1. Dec 17, 2011 #1
    1. The problem statement, all variables and given/known data

    Prove: for any real number x, -|x|[itex]\leq[/itex]x[itex]\leq[/itex]|x|.

    2. Relevant equations

    Only the definition of absolute value is allowed.

    3. The attempt at a solution

    Don't even know where to start
     
  2. jcsd
  3. Dec 17, 2011 #2
    First prove -lxl≤x then prove x≤lxl
     
  4. Dec 18, 2011 #3

    LCKurtz

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    Also consider breaking the problem into two cases, where x ≥ 0 and x < 0.
     
    Last edited: Dec 18, 2011
  5. Dec 18, 2011 #4
    pretty much what mtayab and LCKurtz said
    first take x greater than zero, take x less than zero and take x equal to zero

    this method is called a proof by exhaustion
     
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