The inequality displayed in the image is:

$|x - 9| \leq 2$

This is an absolute value inequality, which means we need to break it down into two separate inequalities, removing the absolute value. The rule for absolute values is:

$|a| \leq b \quad \text{implies} \quad -b \leq a \leq b$

Using this rule on the given inequality:

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

Step-by-step Solution:

1. Add 9 to all parts of the inequality to isolate $x$: $-2 + 9 \leq x - 9 + 9 \leq 2 + 9$ Simplifying the inequality: $7 \leq x \leq 11$

Final Answer:

$x \in [7, 11]$

This means that $x$ can be any value between 7 and 11, inclusive.

Would you like more details or have any questions on this solution?

Here are 5 related questions:

1. How do we handle absolute value inequalities with "greater than" signs?
2. What happens if the inequality is strict, i.e., $|x - 9| < 2$?
3. Can you solve absolute value inequalities that result in no solutions?
4. How do absolute value inequalities relate to intervals on a number line?
5. What would the solution look like if the inequality were $|x - 9| \geq 2$?

Tip: Always remember to check if the inequality symbol is strict or not, as it determines whether you include endpoints in your solution!