I just got Spivak's calculus today, and I'm already stuck on the prologue problems: 1. The problem Find all x for which (x-1)(x-3)>0 2. The attempt at a solution We know that if ab>0, then either a>0 and b>0, or a<0 and b<0. Thus, if a=(x-1) and b=(x-3), then either (x-1)>0 and (x-3)>0, or (x-1)<0 and (x-3)<0. Solving for x would yield four solutions, but only two, x<1 and x>3, are true. Why is this?