Evaluate or simplify the following expression .
`9 - {7 - 24 div (8 + 6 xx 2 - 16)}`

Options

A. `11`
B. `10`
C. `8`
D. `6`

Answer

To simplify the expression \( 9 - \{ 7 - 24 \div (8 + 6 \times 2 - 16) \} \), 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. **Identify the innermost bracket**:
We first look at the expression inside the round brackets: \( 8 + 6 \times 2 - 16 \).

2. **Perform multiplication inside the round bracket**:
- Calculate \( 6 \times 2 = 12 \).
- Now substitute this back into the expression: \( 8 + 12 - 16 \).

3. **Perform addition and subtraction inside the round bracket**:
- First, calculate \( 8 + 12 = 20 \).
- Then, subtract \( 16 \): \( 20 - 16 = 4 \).
- Now we have simplified the round bracket to \( 4 \).

4. **Substitute back into the curly bracket**:
- The expression now looks like: \( 9 - \{ 7 - 24 \div 4 \} \).

5. **Perform the division inside the curly bracket**:
- Calculate \( 24 \div 4 = 6 \).
- Substitute this back into the curly bracket: \( 9 - \{ 7 - 6 \} \).

6. **Perform the subtraction inside the curly bracket**:
- Calculate \( 7 - 6 = 1 \).
- Now the expression is: \( 9 - 1 \).

7. **Final subtraction**:
- Calculate \( 9 - 1 = 8 \).

Thus, the simplified expression evaluates to \( 8 \).