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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.

Learn how to solve the absolute value inequality |h - 5| ≤ 10 using basic algebraic steps. This problem covers absolute value properties and solving linear inequalities. Suitable for students in Grades 7-10.

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