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Math Help - Inequalities help.

  1. #1
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    Inequalities help.

    The equation is x^3-6x^2+5x-12 > 0

    I got my x-intercepts or the root of the equation after factoring: (x+1)(x-3)(x-4)

    Now how exactly would I solve this by putting it in this form:

    -1 < x < 3 and x > 4 or x > -1 and 3 < x < 4

    I am confused as to which one is the right answer, and can you please explain how to correctly choose and determine it?

    Thanks in advance.
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  2. #2
    Senior Member Educated's Avatar
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    Quote Originally Posted by Pupil View Post
    The equation is x^3-6x^2+5x-12 > 0

    I got my x-intercepts or the root of the equation after factoring: (x+1)(x-3)(x-4)



    x^3-6x^2+5x-12 > 0
    I think you factored it wrong somewhere, this equation cannot be factored into such a simplistic form.

    If it were x^3-6x^2+5x+12 > 0 then you factored it correctly.
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  3. #3
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    Quote Originally Posted by Educated View Post
    x^3-6x^2+5x-12 > 0
    I think you factored it wrong somewhere, this equation cannot be factored into such a simplistic form.

    If it were x^3-6x^2+5x+12 > 0 then you factored it correctly.
    Yeah it's +12, I made a typo.

    So which would be the answer and how I about do I go finding the answer for future inequalities? I have read dozens of articles online and nothing shows any way to go about solving these.
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  4. #4
    Senior Member Educated's Avatar
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    Well i'm not good at explaining things but I'll try to explain as best as I can:

    It's the x^3 that tells us which answer it is. It tells us that as x goes to positive infinity, so does y. But if it were -(x^3), then this would tell us that as x goes to positive infinity, y goes to negative infinity.

    Since the x^3 is positive, x would have to be larger than the largest root because it goes to infinity, and so x > 4. When we know this, we know the rest.

    Sorry I'm not better at my explanations.
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  5. #5
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    Quote Originally Posted by Educated View Post
    Well i'm not good at explaining things but I'll try to explain as best as I can:

    It's the x^3 that tells us which answer it is. It tells us that as x goes to positive infinity, so does y. But if it were -(x^3), then this would tell us that as x goes to positive infinity, y goes to negative infinity.

    Since the x^3 is positive, x would have to be larger than the largest root because it goes to infinity, and so x > 4. When we know this, we know the rest.

    Sorry I'm not better at my explanations.
    I am writing this down in my notes, thanks.

    But is there like any practical way to apply your theory to other questions I may have? I thought that too, but as I was looking through my examples my book didn't explain it at all too well and only gave a couple of examples.
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  6. #6
    MHF Contributor harish21's Avatar
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    Hi Pupil,

    You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.
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  7. #7
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    Quote Originally Posted by harish21 View Post
    Hi Pupil,

    You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.
    Thank you Harish, this might be what I've been looking for!
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  8. #8
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    Quote Originally Posted by harish21 View Post
    Hi Pupil,

    You may want to have a look at this thread. Thanks to MHF member Krizalid,this attachment contains nice explanations about inequalities.
    Unfortunately Harish, it wasn't exactly what I was looking for. While it may be a greatly written guide, it seems like the general articles I've found all over the net explaining inequalities and I haven't gotten that deep in this topic yet.

    All I really am looking for is how to determine which one is the answer and why, the way my text book explains it is much too vague with too few examples.
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