|x−2|+4≥13

Sure, let's solve the inequality step by step:

1. |x−2|+4≥13
2. Subtract 4 from both sides to isolate the absolute value: |x−2| ≥ 13 - 4
3. This simplifies to: |x−2| ≥ 9
4. An absolute value inequality is solved by setting up two separate inequalities: x - 2 ≥ 9 and -(x - 2) ≥ 9
5. These simplify to: x ≥ 11 and -x + 2 ≥ 9
6. Solving the second inequality gives: x ≤ -7

So the solution to the inequality |x−2|+4≥13 is x ≥ 11 or x ≤ -7.