Simplify the following :
`-11-[-6-{3-5(8div4-1)}]`.

Answer

To simplify the expression `-11 - [-6 - {3 - 5(8 ÷ 4 - 1)}]`, we will follow the order of operations (BODMAS/BIDMAS). Here’s a step-by-step breakdown of the solution:

### Step 1: Simplify the innermost expression
Start with the innermost operation which is `8 ÷ 4 - 1`.

- Calculate `8 ÷ 4`:
\[ 8 ÷ 4 = 2 \]

- Now substitute back into the expression:
\[ 2 - 1 = 1 \]

### Step 2: Substitute back into the expression
Now replace `8 ÷ 4 - 1` with `1` in the original expression:
\[ -11 - [-6 - {3 - 5(1)}] \]

### Step 3: Simplify the expression inside the curly braces
Now simplify `3 - 5(1)`:
- Calculate `5(1)`:
\[ 5(1) = 5 \]

- Now substitute back:
\[ 3 - 5 = -2 \]

### Step 4: Substitute back into the expression
Now replace `3 - 5(1)` with `-2`:
\[ -11 - [-6 - (-2)] \]

### Step 5: Simplify the expression inside the square brackets
Now simplify `-6 - (-2)`:
- Remember that subtracting a negative is the same as adding:
\[ -6 + 2 = -4 \]

### Step 6: Substitute back into the expression
Now replace `-6 - (-2)` with `-4`:
\[ -11 - (-4) \]

### Step 7: Simplify the final expression
Now simplify `-11 - (-4)`:
- Again, subtracting a negative is the same as adding:
\[ -11 + 4 = -7 \]

### Final Answer
The simplified expression is:
\[ \boxed{-7} \]

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