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Math Help - Solving Inequality

  1. #1
    Senior Member vaironxxrd's Avatar
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    Solving Inequality

    Hello Everyone,

    I have a very embarrassing question. I'm studying the introduction chapter in my Calculus book.

    I have the following problem: (x+2)(x-1)(x-3) > 0

    The answer in my book: (-2,1)\cup(3,8)

    My answer doesn't match and I can't really figure out why:

    (x+2)(x-1)(x-3) > 0

    Split points: -2, 1, 3

    There must be four intervals to test (-\infty,-2), (-2,1), (1,3), and(3,\infty)
    So I use the following test points to determine when the inequality is greater than 0: -3, 0, 2, 4

    x= -3 [-] Doesn't Work
    x = 0 [+] Does Work
    x = 2 [-] Doesn't Work
    x = 4 [+] Does Work

    So according to me and this work I did the solution should be (-2,1) \cup (3,\infty)
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  2. #2
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    Re: Solving Inequality

    Hi,
    Text books are not infallible; in this case you're right and the book is wrong. I'm very prone to arithmetic and algebraic errors, so I almost always check my calculations for such problems by drawing a graph with my graphing software. I suggest you do the same.

    Solving Inequality-mhfcalc11.png
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  3. #3
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    Re: Solving Inequality

    Solving Inequality-01-sep-13.pngproceed like this to consider remaining cases
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