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Math Help - Inequality - x on denominator

  1. #16
    Member SENTINEL4's Avatar
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    A fraction is positive in 2 conditions : a) Numerator and denominator both positive or b) Numerator and denominator both negative.
    If one is positive and the other is negative then the fraction would be negative.

    In your fraction numerator is a standard positive number, so it would be always positive. That means you are in condition (a) above so you need denominator to be positive.


    Quote Originally Posted by Stroodle View Post
    Using the Abstractionists method wouldn't it be 3x+2<6 and  3x+2>0 ??
    Why it should be 3x+2<6?? We talk about the fraction \frac{12}{3x+2}>0 yes? Here you just need to check  3x+2>0 and you have your solution.
    Hope i said it well, because English isn't my mother language
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  2. #17
    Senior Member Stroodle's Avatar
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    Thanks Sentinel, but I meant it for \frac{12}{3x+2}>2

    I should've been clearer
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  3. #18
    Member SENTINEL4's Avatar
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    For \frac{12}{3x+2}>2 \Rightarrow \frac{12}{3x+2}-2>0 \Rightarrow \frac{8-6x}{3x+2}>0 and you take :

    i) 8-6x>0 and 3x+2>0
    ii) 8-6x<0 and 3x+2<0

    You solve i) and ii) and you have for which x it stands...
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