Simplify `92−[18+16÷4{26−(14−7−3)}]`

Options

A. `812/11`
B. `80/496`
C. `700/11`
D. ` 97/14`

Answer

To simplify the expression `92−[18+16÷4{26−(14−7−3)}]`, 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 brackets**:
- We have `(14−7−3)`.
- Calculate:
\[ 14 - 7 = 7 \]
\[ 7 - 3 = 4 \]
- So, `(14−7−3)` simplifies to `4`.

2. **Substitute this back into the expression**:
- The expression now looks like:
\[ 92−[18+16÷4{26−4}] \]

3. **Next, simplify the expression inside the curly brackets**:
- Calculate `26−4`:
\[ 26 - 4 = 22 \]
- Now the expression is:
\[ 92−[18+16÷4×22] \]

4. **Now, handle the division**:
- Calculate `16÷4`:
\[ 16 ÷ 4 = 4 \]
- Substitute back into the expression:
\[ 92−[18+4×22] \]

5. **Next, perform the multiplication**:
- Calculate `4×22`:
\[ 4 × 22 = 88 \]
- Now the expression is:
\[ 92−[18+88] \]

6. **Now, perform the addition inside the brackets**:
- Calculate `18+88`:
\[ 18 + 88 = 106 \]
- Substitute back into the expression:
\[ 92−106 \]

7. **Finally, perform the subtraction**:
- Calculate `92−106`:
\[ 92 - 106 = -14 \]

### Final Answer:
The simplified result of the expression `92−[18+16÷4{26−(14−7−3)}]` is `-14`.