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A really simple inequality, easy to see the solution but hard to prove algebraically.

  1. Dec 17, 2012 #1
    1. The problem statement, all variables and given/known data

    Solve the inequality -9 < 1/x

    A simple inequality, I can see the solution is just x < -1/9 but I can't prove it at all.

    3. The attempt at a solution

    -9 < 1/x

    -9x < 1

    x > -1/9

    Any helpful rules I am forgetting about inequalities? This was a problem in a review from high school set provided by my instructor for my introductory math class. Just curious about a solution, it's a calculus course that doesn't really test on this sort of thing but I figure I should actually try and figure out these basic things.
     
    Last edited: Dec 17, 2012
  2. jcsd
  3. Dec 17, 2012 #2

    Dick

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    Science Advisor
    Homework Helper

    Re: A really simple inequality, easy to see the solution but hard to prove algebraica

    You are forgetting if you multiply both sides by x and x is negative you have to reverse the inequality. Split into two cases x>0 and x<0.
     
  4. Dec 17, 2012 #3
    Re: A really simple inequality, easy to see the solution but hard to prove algebraica

    Oh okay, that makes sense, thanks for the help :).
     
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