Solve for x: |x-6|>7

To solve the inequality |x - 6| > 7, we need to consider two cases: when x - 6 is positive and when it's negative.

Case 1: x - 6 > 7
In this case, we isolate x by adding 6 to both sides of the inequality:
x - 6 + 6 > 7 + 6
x > 13

Case 2: -(x - 6) > 7
Here, we need to distribute the negative sign to x and 6:
-x + 6 > 7

Next, we subtract 6 from both sides of the inequality:
-x + 6 - 6 > 7 - 6
-x > 1

To solve for x, we multiply both sides of the inequality by -1. Since we are multiplying by a negative number, the inequality sign flips:
(-1)(-x) < (1)(-1)
x < -1

Therefore, the solution to |x - 6| > 7 is x > 13 or x < -1.