`92 - [71+{4 – (5 – (4 – 2))}] = ?`

Options

A. 12
B. 21
C. 15
D. 20

Answer

To solve the expression \( 92 - [71 + \{4 - (5 - (4 - 2))\}] \), we will follow the order of operations, which is Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right), often abbreviated as PEMDAS.

### Step-by-Step Solution:

1. **Start with the innermost parentheses**:
\[ 4 - 2 = 2 \]
So, we replace \( (4 - 2) \) with \( 2 \):
\[ 92 - [71 + \{4 - (5 - 2)\}] \]

2. **Next, solve \( 5 - 2 \)**:
\[ 5 - 2 = 3 \]
Now, replace \( (5 - 2) \) with \( 3 \):
\[ 92 - [71 + \{4 - 3\}] \]

3. **Now, solve \( 4 - 3 \)**:
\[ 4 - 3 = 1 \]
Replace \( (4 - 3) \) with \( 1 \):
\[ 92 - [71 + 1] \]

4. **Now, solve \( 71 + 1 \)**:
\[ 71 + 1 = 72 \]
Replace \( (71 + 1) \) with \( 72 \):
\[ 92 - 72 \]

5. **Finally, perform the subtraction**:
\[ 92 - 72 = 20 \]

Thus, the final answer is:
\[ \boxed{20} \]