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Math Help - Absolute Value Inequality

  1. #1
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    Absolute Value Inequality

    |x^2-6x-1|<6

    What I did was:

    -6<x^2-6x-1<6

    -6<x^2-6x-1
    -5<x^2-6x
    -x^2+6x-5<0
    (x-5)(x-1)
    x=5, x=1
    1<x<5

    x^2-6x-1<6
    x^2-6x-7<0
    (x-7)(x+1)<0

    -1<x<7

    The answer given is -1<x<1 or 5<x<7

    Do I have to sketch a graph to visualize it or something to understand it better?
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by fuzzy View Post
    |x^2-6x-1|<6

    What I did was:

    -6<x^2-6x-1<6

    -6<x^2-6x-1
    -5<x^2-6x
    -x^2+6x-5<0
    (x-5)(x-1)
    x=5, x=1
    1<x<5
    all was fine but this last line is wrong. Think why it should be and not 1<x<5.

    x^2-6x-1<6
    x^2-6x-7<0
    (x-7)(x+1)<0

    -1<x<7

    The answer given is -1<x<1 or 5<x<7

    Do I have to sketch a graph to visualize it or something to understand it better?
    did this help?
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  3. #3
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    Quote Originally Posted by fuzzy View Post
    Do I have to sketch a graph to visualize it or something to understand it better?
    You could do that, graph \displaystyle y = |x^2-6x-1|

    Then draw a line through y=6, discard anything above this line.
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  4. #4
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    Quote Originally Posted by abhishekkgp View Post
    did this help?
    Okay. Is the second solution correct?
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  5. #5
    Senior Member abhishekkgp's Avatar
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    Quote Originally Posted by fuzzy View Post
    Okay. Is the second solution correct?
    yup!
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