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Math Help - inequality

  1. #1
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    inequality

    Find the set of real values of x for which :

    \frac{2}{x} \geq 3-x

    I got x=-3 , x=1

    what should I do next ?
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  2. #2
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    Quote Originally Posted by Musab View Post
    Find the set of real values of x for which :

    \frac{2}{x} \geq 3-x

    I got x=-3 , x=1

    what should I do next ?
    Solve the following cases:

    Case 1: x > 0: 2 \geq 3x - x^2 \Rightarrow x^2 - 3x + 2 \geq 0.

    Case 2: x < 0: 2 \leq 3x - x^2 \Rightarrow x^2 - 3x + 2 \leq 0.

    Edit: Note that x \neq 0 (why?)
    Last edited by mr fantastic; September 6th 2008 at 05:43 PM.
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  3. #3
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    Quote Originally Posted by mr fantastic View Post
    Solve the following cases:

    Case 1: x > 0: 2 \geq 3x - x^2 \Rightarrow x^2 - 3x + 2 \geq 0.

    Case 2: x < 0: 2 \leq 3x - x^2 \Rightarrow x^2 - 3x + 2 \leq 0.
    Case 1: x^2 - 3x + 2 \geq 0 \Rightarrow x \leq 1 or x \geq 2 subject to the restriction x > 0. Therefore x \geq 2 or 0 < x \leq 1.

    Case 2: Left for you.
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