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The problem asks to find all possible values of \( a - b \), given the inequalities:

- \( 2 < a < 5 \)
- \( 3 < b < 7 \)

We are tasked with determining the range for \( a - b \).

### Step-by-step solution:

1. **Determine the possible range for \( a - b \):**
   - The minimum value of \( a - b \) occurs when \( a \) is at its smallest (just above 2) and \( b \) is at its largest (just below 7).
     \[
     a_{\text{min}} - b_{\text{max}} = 2 - 7 = -5
     \]
   - The maximum value of \( a - b \) occurs when \( a \) is at its largest (just below 5) and \( b \) is at its smallest (just above 3).
     \[
     a_{\text{max}} - b_{\text{min}} = 5 - 3 = 2
     \]

2. **Final result:**
   The possible values of \( a - b \) range from \( -5 \) to \( 2 \), so:
   \[
   -5 < a - b < 2
   \]

Would you like any further explanation or additional details?

Here are some related questions:
1. What happens if the inequalities change to \( 1 < a < 4 \) and \( 4 < b < 6 \)?
2. How would you find \( a + b \) for the same inequalities?
3. Can you generalize a formula to find \( a - b \) given two inequalities?
4. What if the inequalities are \( 2 \leq a \leq 5 \) and \( 3 \leq b \leq 7 \)? How does it affect the range?
5. How would you approach a similar problem if \( a \) and \( b \) are integers instead of continuous values?

**Tip:** Always pay attention to strict inequalities (e.g., \( < \) vs. \( \leq \)) as they affect the boundary values in your final answer.

Suppose that 2 < a < 5 and 3 < b < 7. Find all possible values of a - b.

Learn how to find the range of values for a - b, given the inequalities 2 < a < 5 and 3 < b < 7. This step-by-step solution covers key algebraic concepts such as inequalities and arithmetic, making it suitable for students in Grades 6-8.

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