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The problem asks for an absolute value equation that represents the range of wind speeds for a Category 1 hurricane, where the minimum speed is 74 miles per hour, and the maximum speed is 95 miles per hour. Let \( v \) represent the wind speed.

### Step-by-step solution:

1. **Find the midpoint between 74 and 95**: 
   The midpoint helps to center the absolute value equation.
   \[
   \text{Midpoint} = \frac{74 + 95}{2} = \frac{169}{2} = 84.5
   \]
   So, the center of the wind speed range is 84.5 miles per hour.

2. **Find the distance from the midpoint to the extremes**:
   The distance to either extreme (74 or 95) is:
   \[
   95 - 84.5 = 10.5 \quad \text{or} \quad 84.5 - 74 = 10.5
   \]
   This is the "radius" of the range around the midpoint.

3. **Set up the absolute value equation**:
   The absolute value equation represents wind speeds within 10.5 miles per hour of 84.5. Thus, the equation is:
   \[
   |v - 84.5| = 10.5
   \]
   
This equation captures the minimum and maximum wind speeds for the Category 1 hurricane.

Would you like more details on how this was derived or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you interpret absolute value equations in real-world situations?
2. What is the significance of the midpoint in the context of an absolute value equation?
3. How can you graph the absolute value equation \( |v - 84.5| = 10.5 \)?
4. How would the equation change if the maximum wind speed were higher?
5. Can you set up a similar equation for a different range of speeds?

**Tip:** In absolute value equations like this one, the number on the right-hand side represents the maximum deviation from the midpoint.

The minimum sustained wind speed of a Category 1 hurricane is 74 miles per hour. The maximum sustained wind speed is 95 miles per hour. Write an absolute value equation that represents the minimum and maximum speeds. Let v represent the wind speed.

Learn how to write an absolute value equation to represent the wind speed range of a Category 1 hurricane, with a minimum of 74 mph and a maximum of 95 mph. This problem covers algebraic concepts like absolute value and range, suitable for students in Grades 7-9.

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