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Math Help - Simplify absolute value

  1. #1
    Newbie
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    Simplify absolute value

    My calculus assignment is asking this:

    If 4x, simplify the expression by removing the absolute sign.
    abs(4 - x) = ?

    It is asking for only a single definite answer. What could this be? I really don't understand.
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  2. #2
    Senior Member
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    Feb 2008
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    Using the definition of the absolute value

    |4-x|=4-x \ \ \ \mbox{if} \ \ 4-x>0

    |4-x|=-(4-x) \ \ \mbox{if} \ \ 4-x<0

    Since 4<x\Rightarrow 4-x<0

    \Rightarrow |4-x|=-(4-x)=x-4
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  3. #3
    MHF Contributor

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    Slightly more succinctly, if 4< x, then 0< x- 4, 0> 4- x.
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