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Math Help - Solving Inequality for X

  1. #1
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    Solving Inequality for X

    I'm trying to solve 1/(2-x) > 1/2 for x, where 0 < x < 1. The problem is, I'm getting x < 0 where as I think it should be x > 0. I know you need to flip the inequality when multiplying or dividing by a negative number, but this isn't coming up at all. What am I missing?

    1/(2-x) > 1/2 Since 0 < x < 1, (2-x) is never negative and multiplying by it does not switch the inequality

    2 > 2 - x

    0 > x
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  2. #2
    Super Member Quacky's Avatar
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    Re: Solving Inequality for X

    Quote Originally Posted by Relmiw View Post
    I'm trying to solve 1/(2-x) > 1/2 for x, where 0 < x < 1. The problem is, I'm getting x < 0 where as I think it should be x > 0. I know you need to flip the inequality when multiplying or dividing by a negative number, but this isn't coming up at all. What am I missing?

    1/(2-x) > 1/2 Since 0 < x < 1, (2-x) is never negative and multiplying by it does not switch the inequality

    2 > 2 - x

    0 > x
    \frac{1}{2-x}>\frac{1}{2}

    Knowing that 2-x>0, we cross multiply:

    2>2-x

    -x<0

    x>0
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  3. #3
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    Re: Solving Inequality for X

    ahhhh, thanks. I should have known. once I got to -x < 0 i would instinctively drop the -1 even knowing i was on the lookout for it
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  4. #4
    Super Member Quacky's Avatar
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    Re: Solving Inequality for X

    Quote Originally Posted by Relmiw View Post
    ahhhh, thanks. I should have known. once I got to -x < 0 i would instinctively drop the -1 even knowing i was on the lookout for it
    I did that too when I first tackled the question.
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