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Absolute Values

  1. Oct 24, 2005 #1
    An example in my textbook gives

    [tex] \vert \frac{5-x}{5x} \vert \Leftrightarrow \frac {1}{5} (\frac{1}{\vert x \vert}) (\vert x-5 \vert) [/tex]

    Is there something I don't know about absolute values that allows [itex] \vert 5-x \vert [/itex] to become [itex] \vert x-5 \vert [/itex] or is this a mistake in the text?
  2. jcsd
  3. Oct 24, 2005 #2


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    What would you say about |x| - |-x|?
  4. Oct 24, 2005 #3
    It would be zero. So [tex] \vert 5 \vert + \vert -x \vert \Longleftrightarrow \vert -5 \vert + \vert x \vert [/tex]

    Thanks for the push.
  5. Oct 24, 2005 #4


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    Well yes, but in your case |5-x| doesn't necessarily equal |5| + |-x|, but it does equal |x-5|, as you asked in the first place.
  6. Oct 24, 2005 #5


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    By definition |a|=|-a|. Let a=x-5 and the result is obvious.
  7. Oct 24, 2005 #6
    [tex]\vert x \vert - \vert-x \vert = 0[/tex]

    The absolute value a number simply means that its positive, no matter what. So abs(x) - (abs(-x) would be the same as abs(x) - abs(x). This is actaully quite usfull in the field of programming.
    Last edited: Oct 24, 2005
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