solve: 22 – [9 – {6 – (10 –4-3 )}]

Options

A. 12
B. 14
C. 16
D. 18

Answer

To solve the expression \( 22 - [9 - \{6 - (10 - 4 - 3)\}] \), we will follow the order of operations, often remembered by the acronym BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Start with the innermost bracket**:
We first solve \( (10 - 4 - 3) \).
\[ 10 - 4 = 6 \]
\[ 6 - 3 = 3 \]
So, \( (10 - 4 - 3) = 3 \).

2. **Substitute back into the expression**:
Now substitute \( 3 \) back into the expression:
\[ 22 - [9 - \{6 - 3\}] \]

3. **Solve the next bracket**:
Now we solve \( \{6 - 3\} \):
\[ 6 - 3 = 3 \]
So, \( \{6 - 3\} = 3 \).

4. **Substitute back into the expression**:
Substitute \( 3 \) back into the expression:
\[ 22 - [9 - 3] \]

5. **Solve the next bracket**:
Now we solve \( [9 - 3] \):
\[ 9 - 3 = 6 \]
So, \( [9 - 3] = 6 \).

6. **Substitute back into the expression**:
Substitute \( 6 \) back into the expression:
\[ 22 - 6 \]

7. **Final subtraction**:
Now we perform the final subtraction:
\[ 22 - 6 = 16 \]

### Final Answer:
The value of the expression \( 22 - [9 - \{6 - (10 - 4 - 3)\}] \) is \( 16 \).

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