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Question 7409: How would I solve the inequality for the equation x - 1/x^2 < 0? I came up with the answer of (0,1). Would this be the correct answer or show me how to work for the correct answer.
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! Try multiplying everything by x^2. That should get you x^3 < 0. Cube root both sides and you'll get x < 0.
If you plug in a positive value, you'll ALWAYS end up this way: "I'll pick the smallest positive number I can think of, but then I'd be subtracting 1/x^2, which is even smaller than my (already) small number. That won't bring me less than zero." So we can't plug in positive numbers.
You can't plug in a zero because that would make a denominator zero in the inequality.
What about negative numbers? It's fairly obvious that if you choose a negative x, you'll even go further to the negative direction by just a little when 1/x^2 is subtracted from it.
So any negative number will work for your inequality.
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