Simplify : `84 - 7[-11x - 4{-17x + 3(8-9+5x))}]`

Answer

To simplify the expression `84 - 7[-11x - 4{-17x + 3(8 - 9 + 5x)}]`, we will follow the order of operations (commonly known as BODMAS/BIDMAS: Brackets, Orders, Division and Multiplication, Addition and Subtraction).

### Step-by-Step Solution:

1. **Start with the original expression**:
\[ 84 - 7[-11x - 4{-17x + 3(8 - 9 + 5x)}] \]

2. **Simplify the innermost bracket**:
\[ 8 - 9 + 5x = -1 + 5x = 5x - 1 \]
Now substitute this back into the expression:
\[ 84 - 7[-11x - 4{-17x + 3(5x - 1)}] \]

3. **Distribute the 3 into the bracket**:
\[ 3(5x - 1) = 15x - 3 \]
Substitute this back:
\[ 84 - 7[-11x - 4{-17x + 15x - 3}] \]

4. **Combine like terms inside the curly braces**:
\[ -17x + 15x = -2x \]
So we have:
\[ 84 - 7[-11x - 4(-2x - 3)] \]

5. **Distribute the -4**:
\[ -4(-2x) = 8x \quad \text{and} \quad -4(-3) = 12 \]
Substitute back:
\[ 84 - 7[-11x + 8x + 12] \]

6. **Combine like terms**:
\[ -11x + 8x = -3x \]
So the expression becomes:
\[ 84 - 7[-3x + 12] \]

7. **Distribute the -7**:
\[ -7(-3x) = 21x \quad \text{and} \quad -7(12) = -84 \]
Substitute back:
\[ 84 + 21x - 84 \]

8. **Combine the constants**:
\[ 84 - 84 = 0 \]
Thus, we have:
\[ 21x \]

### Final Answer:
\[ 21x \]