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Math Help - Inequality

  1. #1
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    Inequality

    Solve the Inequality

    \frac{T-8}{3-T}<0

    I got T<8\quad -T<-3\quad \Longrightarrow T>3

    But the books answers were completely opposte of what I got. I'm not exactly sure where I messed up. The book got  T>8\quad T<3

    Anyone know what I'm doing wrong?
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  2. #2
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    Quote Originally Posted by OzzMan View Post
    Solve the Inequality

    \frac{T-8}{3-T}<0

    I got T<8\quad -T<-3\quad \Longrightarrow T>3

    But the books answers were completely opposte of what I got. I'm not exactly sure where I messed up. The book got  T>8\quad T<3

    Anyone know what I'm doing wrong?
    Your inequality describes a negative fraction.
    A fraction is negative if

    - the numerator is negative (that means lower than zero) and the denominator is positive (that means greater than zero)

    or

    -- the numerator is positive (that means greater than zero) and the denominator is negative (that means lower than zero)

    Transcribe these conditions into inequalities:

    T-8<0~\wedge~3-T>0~~\vee~~T-8>0~\wedge~3-T<0

    \underbrace{T<8~\wedge~3>T}_{T < 3}~~\vee~~ \underbrace{T>8~\wedge~3<T}_{T>8}

    The final result is: T < 3 ~\vee~ T > 8

    To check your calculations you can plug in some values for T to see if they give the right result.
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