Compute the missing number so the equation balances: ? + 1046 − 398 − 69 = 999

Introduction / Context:
This arithmetic problem involves combining constants and isolating the unknown so that both sides of the equation are equal. It assesses accuracy with addition and subtraction, as well as clear organization of steps to avoid small mistakes that can flip a correct answer into an incorrect one.

Given Data / Assumptions:

• Equation: ? + 1046 − 398 − 69 = 999
• All terms are integers and standard order of operations applies (left to right for additions/subtractions).
• Goal: find the single integer replacing the question mark that makes the equation true.

Concept / Approach:
Combine the known numbers first to simplify. Then, isolate the unknown on one side using inverse operations. Keeping track of signs is crucial because a sign error will lead to a wrong value for the unknown.

Step-by-Step Solution:
1) Combine constants: 1046 − 398 − 69.2) First subtraction: 1046 − 398 = 648.3) Second subtraction: 648 − 69 = 579.4) The equation reduces to: ? + 579 = 999, hence ? = 999 − 579 = 420.

Verification / Alternative check:
Substitute back: 420 + 1046 − 398 − 69 = 420 + 579 = 999. The equality holds, verifying the result.

Why Other Options Are Wrong:
514: 514 + 579 = 1093, which overshoots 999 by 94.399: 399 + 579 = 978, which is 21 less than 999.520: 520 + 579 = 1099, which is 100 too large.

Common Pitfalls:
Mixing the order of subtraction, combining 398 and 69 incorrectly, or forgetting that both are subtracted. Always consolidate constants first; then move the result across the equals sign by subtracting from 999 to isolate the unknown cleanly.

Final Answer:
420