Question 7409
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.