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Math Help - how to prove abs(a-b) <= abs(a) + abs(b)?

  1. #1
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    Unhappy how to prove abs(a-b) <= abs(a) + abs(b)?

    Hi guys, Im taking calculus in university but i'm having some trouble with some kinds of problems.

    can some one help me prove this:

    abs(a-b) <= abs(a) + abs(b) for all real numbers of a and b

    i get very confused when i see abs values =((

    thanks in advance
    Last edited by mr fantastic; September 27th 2010 at 06:39 PM. Reason: Deleted excessive ?'s in title.
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  2. #2
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    The standard triangle inequality states that |x+y|\le |x|+|y|.

    So let x=a~\&~y=-b.
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  3. #3
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    Quote Originally Posted by Plato View Post
    The standard triangle inequality states that |x+y|\le |x|+|y|.

    So let x=a~\&~y=-b.
    so do i sub a and -b into the standard triangle inequality equation?? and solve??
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  4. #4
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    i really dont know how to start =(
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  5. #5
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    Quote Originally Posted by sam0812 View Post
    i really dont know how to start =(
    You have been told exactly what to do. What don't you understand about reply #2?

    By the way: http://math.ucsd.edu/~wgarner/math4c...gleinequal.htm
    Last edited by mr fantastic; September 27th 2010 at 06:48 PM. Reason: Added link to proof of triangle inequality.
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  6. #6
    Junior Member pirateboy's Avatar
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    Try assigning actual values to the variables and see if that makes more sense. Try using some easy numbers.

    Maybe let a=2 and b=7.

    Plug that into your original equation and see what happens.
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