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Math Help - solving the equation

  1. #1
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    solving the equation

    Solve:

    2x + 3 = |4x - 7|


    Thanks for your help!
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Mr_Green View Post
    Solve:

    2x + 3 = |4x - 7|


    Thanks for your help!
    There are two cases to consider:

    1. 4x-7>=0

    then we need to solve:

    2x+3 = 4x-7

    which has solution: x=5, which we need to check satisfies the assumed
    condition 4x-7 >=0, which it does so x=5 is a solution.

    2. 4x-7<0

    then we need to solve:

    2x+3 = -(4x-7)

    or:

    6x = 4,

    so x=2/3. Now check this in the assumed condition 4x-7<0, which it passes
    so x=2/3 is also a solution.

    Hence the solutions are x=5, and x=2/3.

    RonL
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  3. #3
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    Quote Originally Posted by Mr_Green View Post
    Solve:

    2x + 3 = |4x - 7|


    Thanks for your help!
    Use the fact that,
    \sqrt{x^2}=|x|
    Thus,
    2x+3=\sqrt{(4x-7)^2}
    Square,
    (2x+3)^2=(4x-7)^2
    This is a quadradic equation, solve via quadradic formula.
    Last edited by ThePerfectHacker; February 3rd 2007 at 04:02 PM.
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