The given inequality is:

$|x - 2| \geq 11$

To solve this absolute value inequality, we can break it into two cases:

Case 1: $x - 2 \geq 11$

Solve for $x$: $x - 2 \geq 11$ $x \geq 11 + 2$ $x \geq 13$

Case 2: $-(x - 2) \geq 11$ or $x - 2 \leq -11$

Solve for $x$: $x - 2 \leq -11$ $x \leq -11 + 2$ $x \leq -9$

Final Solution:

The solution set is: $x \leq -9 \quad \text{or} \quad x \geq 13$

This means that $x$ can be any number less than or equal to $-9$ or greater than or equal to $13$.

Would you like more details or have any further questions?

Here are 5 related questions for practice:

1. Solve $|x + 3| \geq 5$.
2. Solve $|2x - 1| \leq 7$.
3. Find the solution for $|3x + 5| = 9$.
4. Determine the solution for $|x - 4| \leq 8$.
5. Solve the quadratic inequality $|x^2 - 4x| > 10$.

Tip: For absolute value inequalities, remember that the inequality splits into two cases based on the definition of absolute value: one for the positive case and another for the negative case.