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Math Help - Logic proof question

  1. #1
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    Logic proof question

    if (x/(x-1)) \leq 2 , then x < 1or x \geq 2.

    Im not sure how to prove this.

    I tried this method here from the user xalk, but it didnt seem to work for this question even though this one is similar.

    http://www.mathhelpforum.com/math-he...gic-proof.html
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  2. #2
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    Here's a start

     \frac{x}{x-1} \leq 2

     x \leq 2(x-1)

     x \leq 2x-2

    Now solve for x.
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  3. #3
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    Quote Originally Posted by p00ndawg View Post
    if (x/(x-1)) \leq 2 , then x < 1or x \geq 2.

    Im not sure how to prove this.

    I tried this method here from the user xalk, but it didnt seem to work for this question even though this one is similar.

    http://www.mathhelpforum.com/math-he...gic-proof.html
    So \frac{x}{x-1}\leq 2

    What if x>1? Then x\leq 2(x-1)\rightarrow x\leq 2x-2\rightarrow -x\leq -2\rightarrow x\geq 2 So if x>1, x must be \geq 2

    Try something similar for x<1
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