Solve the inequality:2<|x-3|<=5

Answer 1

2 < l x-3 l ≤ 5 means that l x - 3 l ≤ 5 AND l x - 3 l > 2

If l x - 3 l ≤ 5, then -5 ≤ x - 3 ≤ 5. So, -2 ≤ x ≤ 8.

If l x - 3 l > 2, then x - 3 > 2 or x - 3 < -2. So, x > 5 or x < 1

Solution set: [-2,1) ∪ (5,8]