`{52-(9-2)} div [3 xx {1+(-2) xx (-2)}]=`?

Options

A. 3
B. `-9`
C. 9
D. `-5`

Answer

To solve the equation `{52 - (9 - 2)} ÷ [3 × {1 + (-2) × (-2)}]`, we will follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

### Step-by-Step Solution:

1. **Evaluate the expression inside the first set of parentheses:**
\[ 9 - 2 = 7 \]
So, the expression now becomes:
\[ 52 - 7 \]

**Hint:** Always start by simplifying expressions inside parentheses.

2. **Subtract from 52:**
\[ 52 - 7 = 45 \]
Now, we have:
\[ 45 ÷ [3 × {1 + (-2) × (-2)}] \]

**Hint:** Perform the subtraction carefully to avoid mistakes.

3. **Evaluate the expression inside the second set of parentheses:**
\[ (-2) × (-2) = 4 \]
So, we can rewrite the expression as:
\[ 1 + 4 = 5 \]

**Hint:** Remember that multiplying two negative numbers results in a positive number.

4. **Now substitute back into the expression:**
\[ 45 ÷ [3 × 5] \]

**Hint:** Always replace the evaluated expressions back into the main equation to keep it clear.

5. **Multiply inside the brackets:**
\[ 3 × 5 = 15 \]
Now, the expression simplifies to:
\[ 45 ÷ 15 \]

**Hint:** Multiplication should be done before division as per the order of operations.

6. **Finally, perform the division:**
\[ 45 ÷ 15 = 3 \]

**Hint:** Division is the last operation to perform in this case.

### Final Answer:
The value of the expression is **3**.