Find the unknown that satisfies the equation: ? + 6207 − 9038 = 107

Introduction / Context:
This problem asks you to determine the unknown that balances an equation composed of two subtractions around a single addition. It checks comfort with integer arithmetic and the ability to rearrange equations systematically without introducing sign errors.

Given Data / Assumptions:

• Given relation: ? + 6207 − 9038 = 107
• All values are integers.
• Goal: solve for the unknown represented by the question mark.

Concept / Approach:
Combine the known constants first to simplify. Recognize that 6207 − 9038 is negative, so the unknown must offset that deficit to achieve 107. Then isolate the unknown by moving the combined constant to the other side of the equation with the opposite sign.

Step-by-Step Solution:
1) Compute the constant part: 6207 − 9038 = −2831.2) The equation becomes: ? − 2831 = 107.3) Add 2831 to both sides to isolate the unknown: ? = 107 + 2831.4) Evaluate: 107 + 2831 = 2938.

Verification / Alternative check:
Substitute the result: 2938 + 6207 − 9038 = 2938 − 2831 = 107. The equality holds, confirming correctness.

Why Other Options Are Wrong:
2724: Yields 2724 − 2831 = −107, not 107.2814: Yields 2814 − 2831 = −17, not 107.None of these: Not applicable since 2938 exactly satisfies the equation.

Common Pitfalls:
Forgetting that 6207 − 9038 is negative; flipping the sign when moving terms; or adding the wrong pair of numbers during the final step. Keep the structure ? − 2831 = 107 clear to avoid mistakes.

Final Answer:
2938