`1 - [5 - {2 + (-5 + 6 - 2)2}]` is equal to :

Options

A. -4
B. 2
C. 0
D. -2

Answer

To solve the expression \(1 - [5 - \{2 + (-5 + 6 - 2) \cdot 2\}]\), we will follow the order of operations, often remembered by the acronym BODMAS/BIDMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Simplify the innermost bracket**:
\[ -5 + 6 - 2 \]
Calculate:
\[ -5 + 6 = 1 \]
Then:
\[ 1 - 2 = -1 \]
So, we have:
\[ -5 + 6 - 2 = -1 \]

2. **Substitute back into the expression**:
Now, replace \((-5 + 6 - 2)\) with \(-1\):
\[ 1 - [5 - \{2 + (-1) \cdot 2\}] \]

3. **Calculate the multiplication**:
Now, calculate \((-1) \cdot 2\):
\[ -1 \cdot 2 = -2 \]
Substitute this back into the expression:
\[ 1 - [5 - \{2 - 2\}] \]

4. **Simplify the expression inside the curly brackets**:
\[ 2 - 2 = 0 \]
So now we have:
\[ 1 - [5 - 0] \]

5. **Simplify the expression inside the square brackets**:
\[ 5 - 0 = 5 \]
Now substitute this back:
\[ 1 - 5 \]

6. **Final subtraction**:
\[ 1 - 5 = -4 \]

### Final Answer:
The value of the expression \(1 - [5 - \{2 + (-5 + 6 - 2) \cdot 2\}]\) is \(-4\).