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.

Learn how to solve the absolute value inequality ∣x−9∣≥2 step-by-step. This solution covers key algebraic concepts and theorems related to absolute value inequalities, including splitting the inequality into two cases. Suitable for students in Grades 8-10.

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