I have a question about inequalities like 1/x < 4. In this case the answer is (neg infinity, 0) U (1/4, pos infinity). It's intuitive that the set of negatives should be included, but the mechanical process of solving for x just goes out the window. That is, what rule do I break if i were to just solve for x... x>1/4 so the set would be simply (1/4, pos infinity). And, how do i know when the solving for x alone will not work.