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Math Help - inequality help

  1. #1
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    inequality help

    x^2 - 4x < 5

    = x - 4x < sqrt(5)

    = -3x < sqrt(5)

    = x > sqrt(5)/3

    surely this is wrong!! any help thank u
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  2. #2
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    I would start this way:

    x^2 - 4x - 5 < 0

    (x - 5)(x + 1) < 0

    Can you finish from here?
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  3. #3
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    Quote Originally Posted by icemanfan View Post
    I would start this way:

    x^2 - 4x - 5 < 0

    (x - 5)(x + 1) < 0

    Can you finish from here?
    ah yees yes i understand what u did. yeah i can finish it. thank u!
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  4. #4
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    Quote Originally Posted by icemanfan View Post
    I would start this way:

    x^2 - 4x - 5 < 0

    (x - 5)(x + 1) < 0

    Can you finish from here?


    x < 5 , x < -1 is that it ?
    Last edited by jvignacio; October 2nd 2008 at 08:42 PM.
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  5. #5
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    Quote Originally Posted by jvignacio View Post
    x < 5 , x <= -2 is that it ?
    No. Draw the graph of y = (x - 5)(x + 1). For what values of x is y < 0 ....? That is, for what values of x is the graph below the x-axis ....?

    Answer: -1 < x < 5.
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    No. Draw the graph of y = (x - 5)(x + 1). For what values of x is y < 0 ....? That is, for what values of x is the graph below the x-axis ....?

    Answer: -1 < x < 5.
    or x < 5 and x > -1 ????
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  7. #7
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    Quote Originally Posted by jvignacio View Post
    or x < 5 and x > -1 ????
    I suppose so. But it's a poor way of stating the correct answer and could easily be misunderstood.
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  8. #8
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    Not necessary to make a sketch, just complete the square:

    x^{2}-4x-5<0\implies (x-2)^{2}<9\implies -3<x-2<3, and we're done.
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