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The problem asks to write an absolute value equation to represent the minimum and maximum heights of a handrail, with the minimum height being 30 inches and the maximum height being 38 inches.

### Approach:
1. **Step 1**: Find the midpoint between the minimum and maximum heights. This is the average of the two values:
   \[
   \text{midpoint} = \frac{30 + 38}{2} = 34
   \]

2. **Step 2**: Calculate the distance from the midpoint to the minimum and maximum heights. This distance will serve as the value of deviation from the center point:
   \[
   \text{deviation} = 38 - 34 = 4
   \]

3. **Step 3**: Form the absolute value equation. The absolute value will represent how far \( h \) (the height) can deviate from the midpoint of 34 by no more than 4 inches:
   \[
   |h - 34| = 4
   \]

### Final Answer:
The absolute value equation is:
\[
|h - 34| = 4
\]

This equation means that the height \( h \) can range from 30 inches to 38 inches.

Would you like any further explanation, or do you have any questions?

### Related Questions:
1. How do you solve absolute value equations?
2. Can the absolute value function represent other ranges beyond this specific example?
3. How do you graph absolute value equations?
4. How do you find the midpoint between two numbers in general?
5. How would this change if the maximum and minimum heights were different?

**Tip:** The number inside the absolute value represents the midpoint, while the number outside determines how far the value can deviate.

A safety regulation states that the minimum height of a handrail is 30 inches. The maximum height is 38 inches. Write an absolute value equation that represents the minimum and maximum heights, h.

Learn how to form an absolute value equation to represent the minimum and maximum heights of a handrail, with details on calculating the midpoint and deviation. Suitable for middle school students in grades 7-9.

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