The inequality shown in the image is:

$|x + 2| > 9$

To solve this absolute value inequality, we break it into two cases based on the definition of absolute value:

1. $x + 2 > 9$
2. $x + 2 < -9$

Case 1:

Solve $x + 2 > 9$: $x > 9 - 2$ $x > 7$

Case 2:

Solve $x + 2 < -9$: $x < -9 - 2$ $x < -11$

Thus, the solution to the inequality $|x + 2| > 9$ is: $x > 7 \quad \text{or} \quad x < -11$

This means $x$ must be either greater than 7 or less than -11.

Would you like more details or have any questions?

Here are some related questions to expand your understanding:

1. How would you solve $|x - 5| > 12$?
2. What happens if the inequality is $|x + 2| \leq 9$ instead?
3. Can absolute value inequalities have no solution?
4. How can you graph the solution of $|x + 2| > 9$ on a number line?
5. How do you interpret the solution of an inequality involving absolute values in real-world contexts?

Tip: When solving absolute value inequalities, always remember to handle both the positive and negative cases separately.