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Math Help - Graphing Inequalities? Solution sets?

  1. #1
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    Graphing Inequalities? Solution sets?

    Thanks for all your help...I don't understand this one....

    How do I graph it?

    x^2 < or = x + 12

    I factored it into (x+3)(x-4) < or = 0

    My teacher taught me to make number lines for each factor and put where the factor is positive or negative and I still don't get it. Can anyone explain how those sign graphs work?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Dunit0001 View Post
    Thanks for all your help...I don't understand this one....

    How do I graph it?

    x^2 < or = x + 12

    I factored it into (x+3)(x-4) < or = 0

    My teacher taught me to make number lines for each factor and put where the factor is positive or negative and I still don't get it. Can anyone explain how those sign graphs work?
    you have: x^2 \le x + 12

    \Rightarrow x^2 - x - 12 \le 0

    just graph the parabola y = x^2 - x - 12 it will be easy to identify the interval where it is less than or equal to zero (on this interval, the graph will be below the x-axis). so the answer is the range of x's for which the graph is under the x-axis (this includes the end points, since we can be equal to zero)

    this will indeed be easier if you consider the factors (x + 3)(x - 4). this is zero for x = -3, and x = 4. now check all regions in between those and on either side to see if the inequality holds (your professor was trying to emphasize the concept that we have a number less than zero if we have a positive times a negative, so just make sure one is negative while the other is positive)
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