The given sum notation is:

\[
\sum_{k=4}^{9} (7 - k)
\]

This means we need to compute the sum of \( (7 - k) \) as \( k \) takes values from 4 to 9 (inclusive). Let’s calculate the values step-by-step.

For each value of \( k \):

- \( k = 4 \), \( 7 - 4 = 3 \)
- \( k = 5 \), \( 7 - 5 = 2 \)
- \( k = 6 \), \( 7 - 6 = 1 \)
- \( k = 7 \), \( 7 - 7 = 0 \)
- \( k = 8 \), \( 7 - 8 = -1 \)
- \( k = 9 \), \( 7 - 9 = -2 \)

Now, sum these values:

\[
3 + 2 + 1 + 0 - 1 - 2 = 3
\]

Therefore, the value of the sum is:

\[
\boxed{3}
\]

Would you like more details on summation? Here are a few related questions to explore further:

1. What are the properties of summation notation?
2. How does summation apply to geometric sequences?
3. Can summation be used for integrals in calculus?
4. What happens if you change the limits of summation?
5. How does summation apply in series expansion?

**Tip:** Always double-check the range of summation to avoid missing any terms!

Discover how to compute the sum of (7 - k) from k=4 to k=9. This problem explores the use of summation notation and arithmetic sequences in basic algebra, ideal for students in Grades 6-8. Includes a detailed step-by-step solution and key mathematical concepts.

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