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The given expression involves two summations:

\[
\sum_{k=7}^{12} (3k - 9) + \sum_{k=-2}^{3} (1 - 4k)
\]

- The first summation from \( k = 7 \) to \( k = 12 \) results in \( 117 \).
- The second summation from \( k = -2 \) to \( k = 3 \) results in \( -6 \).

Thus, the total sum is:

\[
117 + (-6) = 111
\]

Would you like further details or have any questions about the steps? 

Here are five related questions you might find helpful:
1. How do you break down summations into individual terms?
2. What are some common properties of summations?
3. How does changing the range of summation affect the result?
4. Can summations be computed using different techniques (e.g., partial sums)?
5. How do you interpret double summations in different contexts?

**Tip:** When computing summations, it's useful to check for arithmetic series patterns, which can simplify the calculation.

Evaluate the expression: \(\sum_{k=7}^{12} (3k - 9) + \sum_{k=-2}^{3} (1 - 4k)\)

Learn how to evaluate two summations: \(\sum_{k=7}^{12} (3k - 9)\) and \(\sum_{k=-2}^{3} (1 - 4k)\), involving arithmetic expressions. This problem covers key mathematical concepts, including summation formulas and arithmetic progression properties. Suitable for students in Grades 9-12.

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