Careful bracket evaluation — nested subtraction Simplify the expression: 6 − [9 − {18 − (15 − 12 − 9)}].

Introduction / Context:
Nestled parentheses with multiple minus signs commonly produce sign errors. The key is to evaluate from the innermost bracket outward and apply subtraction carefully at each level.

Given Data / Assumptions:

• Expression: 6 − [9 − {18 − (15 − 12 − 9)}].
• Standard operation order: parentheses/brackets first; proceed left to right for subtraction within the same level.

Concept / Approach:
Resolve the innermost parentheses, then move outward step by step, watching sign changes when subtracting a negative result.

Step-by-Step Solution:
Innermost: (15 − 12 − 9) → 15 − 12 = 3; 3 − 9 = −6.Next: {18 − (…)} = 18 − (−6) = 18 + 6 = 24.Then: [9 − {…}] = 9 − 24 = −15.Finally: 6 − [ … ] = 6 − (−15) = 6 + 15 = 21.

Verification / Alternative check:
Rewrite as 6 − 9 + {18 − (15 − 12 − 9)}; compute inner part as 24; then 6 − 9 + 24 = 21.

Why Other Options Are Wrong:
Values like 4, 5, 3, or 1 arise from sign mistakes, such as treating 18 − (−6) as 12 or dropping the final negative in 9 − 24.

Common Pitfalls:
Not handling “minus a negative” correctly; skipping the left-to-right evaluation inside the innermost parentheses.

Final Answer:
21