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Math Help - absolute value problem

  1. #1
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    absolute value problem

    Solve: | x - 3 | + | 3 - x | = 12
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  2. #2
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    Smile

    see what happen to the equation when x \geq 3 and x \leq 3
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  3. #3
    Super Member Quacky's Avatar
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    | x - 3 | + | 3 - x | = 12
    Either x-3 or 3-x will be positive. The other will be the negative of the other answer.
    For example, if x=1,
    x-3=-2
    3-x=2
    You can prove this algebraicly by saying that:
    x-3=y
    x=3+y
    x-y=3
    -y=3-x

    Because you're taking the modulus of the answer, you'll end up with the same number twice.
    Eg
    |-2| = 2
    |2| = 2
    so |x-3|=|3-x|

    To get an answer of 12,
    |x-3|=6 and |3-x|=6
    x=9 or x=-3
    Last edited by Quacky; December 23rd 2009 at 07:03 AM. Reason: Added detail for clarification
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