Question:

It takes no more than 40 minutes to run a race, but at least 30 minutes. What equation will model this in \( m \) minutes?

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To express a range of values using absolute value, calculate the distance between the middle point and the boundaries.
Updated On: Sep 30, 2025
  • \( |m - 35|<5 \)
  • \( |m - 35|>5 \)
  • \( |m + 35|<5 \)
  • \( |m + 35|>5 \)
  • \( |m - 35| = 5 \)
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The Correct Option is A

Solution and Explanation

Step 1: Analyze the given constraints.
The time to run the race is between 30 and 40 minutes, so we have the inequality: \[ 30 \leq m \leq 40. \]

Step 2: Express this in an absolute value form.
The middle value is 35, so the time \( m \) is within 5 minutes of 35. Hence, the equation is: \[ |m - 35|<5. \]

Step 3: Conclusion.
Thus, the correct model is \( |m - 35|<5 \), which corresponds to option (A).
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