1. The problem statement, all variables and given/known data I am doing the HW in Spivak's calculus (problem 4 (ii) ) on inequalities. The problem statement is: find all x for which 5-x2 > 8 3. The attempt at a solution I know this is a simple problem, but bear with me for a moment. I want someone who is familiar with Spivak to tell me what the right way to do this is. Pretend for a moment that I know virtually nothing (it shouldn't be too hard ) and that all that I know comes from the first chapter in Spivak's textbook. I start the solution like this 5-x2<8 5-x2 + x2 -8 < 8 + x2 - 8 x2 > -3 Now, I am not sure how to 'rigorously' finish the solution. It is clear that this is true for all numbers x. Is it enough to say that x2 = x*x and since we already showed in a previous example that ab > 0 if a,b > 0 OR a,b < 0. Is that the RIGHT way to do this? Thanks. I am still trying to get a feel for this text and to answer the problems without using any of my prior knowledge.