The inequality shown in the image is:

$|x - 3| \leq 12$

To solve this absolute value inequality, we use the fact that:

$|A| \leq B \quad \text{implies} \quad -B \leq A \leq B$

Here, $A = x - 3$ and $B = 12$. Applying this to the inequality, we have:

$-12 \leq x - 3 \leq 12$

Now, solve for $x$ by adding 3 to all parts of the inequality:

$-12 + 3 \leq x \leq 12 + 3$

$-9 \leq x \leq 15$

Thus, the solution to the inequality is:

$x \in [-9, 15]$

Would you like more details or have any questions?

Here are 5 related questions to expand on this:

1. How do you solve absolute value inequalities with "greater than" signs?
2. Can you explain what happens when the absolute value inequality has a "strict" inequality, like $|x - 3| < 12$?
3. What are some real-world applications of absolute value inequalities?
4. How would you graph the solution to this inequality on a number line?
5. How do we solve absolute value equations, such as $|x - 5| = 10$?

Tip: When solving absolute value inequalities, always check whether the inequality is "less than" or "greater than" to use the correct approach!