- #1

Gamerex

- 25

- 0

**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?