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The problem asks for an inequality that represents Carlos's total exercise time, which is at least 40 minutes. 

- Let \( r \) be the number of laps he runs.
- Let \( s \) be the number of laps he swims.
- Each lap he runs takes him 3 minutes, and each lap he swims takes him 2 minutes.
  
The total time he spends exercising is the time spent running plus the time spent swimming:
- Time running: \( 3r \) (since each running lap takes 3 minutes),
- Time swimming: \( 2s \) (since each swimming lap takes 2 minutes).

Carlos wants to exercise for **at least 40 minutes**, which leads to the inequality:
\[
3r + 2s \geq 40
\]
This inequality states that the total time Carlos spends exercising must be at least 40 minutes.

Would you like further details on this solution?

Here are 5 related questions to deepen your understanding:
1. If Carlos runs 8 laps, how many swimming laps does he need to swim to meet his goal of at least 40 minutes?
2. What happens if Carlos decides to increase his running speed, reducing each lap to 2.5 minutes?
3. How many different combinations of running and swimming laps satisfy the inequality?
4. What would the inequality be if Carlos aimed to exercise for exactly 40 minutes instead of at least 40 minutes?
5. If each lap of swimming took Carlos 3 minutes, how would the inequality change?

**Tip:** When solving inequalities, pay attention to whether the inequality symbol is “greater than or equal to” (≥) or “less than or equal to” (≤), as it can change the solution set.

For his exercise today, Carlos plans to both run and swim. Let r be the number of laps he runs and let s be the number of laps he swims. Each lap he runs takes him 3 minutes, and each lap he swims takes him 2 minutes. He wants to exercise for at least 40 minutes today. Using the values and variables given, write an inequality describing this.

Learn how to create an inequality to represent the total time Carlos spends exercising by running and swimming. This problem involves algebraic concepts such as inequalities, helping students in Grades 6-8 develop their skills in solving real-world problems.

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