|х-6|>1

To solve the inequality |x-6| > 1, we need to consider two different cases:

Case 1: (x-6) > 1 In this case, we have: x - 6 > 1 Adding 6 to both sides, we get: x > 7

Case 2: (x-6) < -1 In this case, we have: x - 6 < -1 Adding 6 to both sides, we get: x < 5

So the solution to the inequality |x-6| > 1 is x > 7 or x < 5.