Simplify : `8.7 -[ 7.6 -{6.5 - (5.4 -(4.3 -2))}]`

Answer

To simplify the expression `8.7 -[ 7.6 -{6.5 - (5.4 -(4.3 -2))}]`, we will follow the order of operations, which requires us to solve the innermost brackets first and work our way outwards.

### Step-by-Step Solution:

1. **Start with the innermost bracket**:
- We have `(4.3 - 2)`.
- Calculate:
\[ 4.3 - 2 = 2.3 \]
- Now, replace `(4.3 - 2)` with `2.3` in the expression:
\[ 8.7 - [7.6 - {6.5 - (5.4 - 2.3)}] \]

2. **Next, solve the next innermost bracket**:
- We have `(5.4 - 2.3)`.
- Calculate:
\[ 5.4 - 2.3 = 3.1 \]
- Replace `(5.4 - 2.3)` with `3.1` in the expression:
\[ 8.7 - [7.6 - {6.5 - 3.1}] \]

3. **Now, solve the next bracket**:
- We have `{6.5 - 3.1}`.
- Calculate:
\[ 6.5 - 3.1 = 3.4 \]
- Replace `{6.5 - 3.1}` with `3.4` in the expression:
\[ 8.7 - [7.6 - 3.4] \]

4. **Next, solve the remaining bracket**:
- We have `[7.6 - 3.4]`.
- Calculate:
\[ 7.6 - 3.4 = 4.2 \]
- Replace `[7.6 - 3.4]` with `4.2` in the expression:
\[ 8.7 - 4.2 \]

5. **Finally, perform the last subtraction**:
- Calculate:
\[ 8.7 - 4.2 = 4.5 \]

### Final Answer:
The simplified result of the expression `8.7 -[ 7.6 -{6.5 - (5.4 -(4.3 -2))}]` is **4.5**.