Question

What is the solution set of this inequality 1<|x-2|<5?

Answer 1

To find the solution set of the inequality 1 < |x - 2| < 5, we need to break it down into two separate inequalities:

1. x - 2 > 1: This gives us x > 3.

2. -(x - 2) > 1: Simplifying, we get -x + 2 > 1, which leads to -x > -1. Multiplying both sides by -1 (and reversing the inequality), we have x < 1.

Combining the two inequalities, the solution set is 1 < x < 3.