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.