The given inequality is $|x - 9| \geq 2$.

To solve an absolute value inequality of the form $|A| \geq B$, we consider two cases:

Case 1: $x - 9 \geq 2$

$x \geq 2 + 9$ $x \geq 11$

Case 2: $-(x - 9) \geq 2$ or $x - 9 \leq -2$

$x \leq 9 - 2$ $x \leq 7$

Thus, the solution is the union of the two cases: $x \leq 7 \quad \text{or} \quad x \geq 11$

In interval notation, the solution is: $(-\infty, 7] \cup [11, \infty)$

Would you like more details or have any questions?

Here are 5 related questions to expand on this topic:

1. How would the solution change if the inequality was $|x - 9| > 2$?
2. What would the solution be for $|x - 9| \leq 2$?
3. Can you graph the solution set on a number line?
4. How do we solve absolute value equations, such as $|x - 9| = 2$?
5. How does the inequality change if it's $|x + 9| \geq 2$?

Tip: Always remember that absolute value inequalities result in two cases, one for the positive and one for the negative.