Question

What is the solution set for |x – 2|– 1 > 2?

Answer 1

First, rewrite this as \(|x-2|>3\). Then, by the definition of absolute value, \(x-2 > 3\) or \(x-2<-3\). If you solve both of these, you find that \(x>5\) or \(x<-1\).

Answer 2

If you want this in set-builder notation, write\[\{x \in \mathbb{R} | \;\;x<-1\quad \text{or}\quad x>5\}\]