We are tasked with solving the absolute value inequality:

$|h - 5| \leq 10$

To solve this, we can break it into two cases because the absolute value represents the distance from $h - 5$ to 0. The inequality $|h - 5| \leq 10$ implies:

$-10 \leq h - 5 \leq 10$

Step 1: Solve the inequality

We now solve for $h$ by adding 5 to all sides of the inequality:

$-10 + 5 \leq h - 5 + 5 \leq 10 + 5$

This simplifies to:

$-5 \leq h \leq 15$

Final Answer:

The solution to the inequality is:

$h \in [-5, 15]$

Let me know if you would like more details or have any questions!

Here are 5 related questions you might be interested in:

1. How do you solve absolute value inequalities in the form $|x - a| \leq b$?
2. What is the difference between $|x - a| \leq b$ and $|x - a| \geq b$?
3. Can absolute value inequalities ever have no solution?
4. What are some real-world applications of absolute value inequalities?
5. How do we graph the solution $-5 \leq h \leq 15$ on a number line?

Tip: When solving absolute value inequalities, always consider both the positive and negative scenarios by breaking them into two separate inequalities.