Evaluate the nested brackets accurately: Compute 10 − [9 − {8 − (7 − 6)}] − 5 and choose the correct integer result.

Introduction / Context:
Nesting of parentheses, braces, and brackets demands inside-out evaluation. This problem reinforces the disciplined approach to evaluate the innermost operation first and move outward step by step to avoid sign mistakes.

Given Data / Assumptions:

• Expression: 10 − [9 − {8 − (7 − 6)}] − 5.
• Standard order: parentheses, then braces, then brackets, then remaining operations left to right.

Concept / Approach:
Work from the innermost parentheses outward. Keep track of minus signs carefully: subtracting a bracketed value changes signs when distributing over the terms inside.

Step-by-Step Solution:
Innermost: (7 − 6) = 1.Next: {8 − 1} = 7.Next: [9 − 7] = 2.Final: 10 − 2 − 5 = 8 − 5 = 3.

Verification / Alternative check:
Rewrite as 10 − 2 − 5 after evaluating the bracketed value to ensure no sign inversion errors. This still equals 3.

Why Other Options Are Wrong:
−5 results from sign mishandling; 1 and 9 arise from partially completed or incorrectly ordered steps; 5 ignores the second subtraction.

Common Pitfalls:
Dropping brackets early; forgetting that subtracting a bracket is subtracting the entire evaluated result; arithmetic slips in the final subtraction.

Final Answer:
3