Question

What is the solution of |x – 2| > –3

Answer 1

Answer: The solution is the set of all real numbers (there are infinitely many solutions).

The reason why this is the case is because |x| is never negative. The smallest it can get is 0, which is larger than -3. That applies to |x-2| as well. So |x-2| is ALWAYS larger than -3 no matter what you pick for x. The smallest |x-2| can get is 0 and that happens when x = 2. Otherwise, the result is some positive value which is larger than -3.

So that's why |x-2| > -3 has infinitely many solutions. We can replace x with any real number we want, and the inequality would be true.