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The problem provides the following inequalities:

- \( 3 < a < 6 \)
- \( 6 < b < 8 \)

You are asked to find all possible values for \( b - a \).

### Step 1: Understand the range of \( b - a \)
The range for \( a \) is between 3 and 6, and the range for \( b \) is between 6 and 8. To find the possible values of \( b - a \), you subtract \( a \) from \( b \).

### Step 2: Analyze boundary values
The maximum value of \( b - a \) will occur when \( b \) is at its maximum (close to 8) and \( a \) is at its minimum (close to 3):

\[
b - a = 8 - 3 = 5
\]

The minimum value of \( b - a \) will occur when \( b \) is at its minimum (close to 6) and \( a \) is at its maximum (close to 6):

\[
b - a = 6 - 6 = 0
\]

### Step 3: Conclusion
Thus, the possible values of \( b - a \) range from \( 0 \) to \( 5 \).

\[
0 < b - a < 5
\]

Would you like more details or further clarification?

Here are 5 related questions:
1. What happens to the value of \( b - a \) if we change the boundaries for \( a \)?
2. How can we interpret the range of \( b - a \) geometrically?
3. Can \( b - a \) ever be negative based on the given conditions?
4. How would the solution change if the inequalities were strict or non-strict (e.g., \( \leq \) instead of \( < \))?
5. What if \( b \) had a smaller maximum range, how would that affect the outcome?

**Tip**: Always examine the boundary values carefully, as they often provide critical information for solving inequality-based problems.

Given 3 < a < 6 and 6 < b < 8, find all possible values of b - a.

Explore how to find all possible values for b - a given the inequalities 3 < a < 6 and 6 < b < 8. This problem involves understanding boundary values and solving expressions involving inequalities. Suitable for students in Grades 7-9.

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