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Simplify the following expression:

[tex]\[
[-2 + (-12) \div (-4)] \times (-6) + \left[ 8 - \left[ 11 - \frac{(9+1)}{-2} \right] \div (-4) \right]
\][/tex]

Sagot :

GinnyAnsweridn
Of course, let's solve the expression step by step:

The given expression is:
[tex]\[ [-2 + (-12) \div (-4)] \times (-6) + [8 - [11 - (9 + 1) \div (-2)] \div (-4)] \][/tex]

### Simplify Inside the Brackets
1. Start with the innermost brackets:
[tex]\[ 9 + 1 = 10 \][/tex]
and plug it back in:
[tex]\[ [11 - 10 \div (-2)] \][/tex]

2. Perform the division:
[tex]\[ 10 \div (-2) = -5 \][/tex]
and substitute it back:
[tex]\[ [11 - (-5)] \][/tex]

3. Simplify the subtraction:
[tex]\[ 11 - (-5) = 11 + 5 = 16 \][/tex]
Plug it back:
[tex]\[ 8 - 16 \div (-4) \][/tex]

4. Perform the division:
[tex]\[ 16 \div (-4) = -4 \][/tex]
and substitute it back:
[tex]\[ 8 - (-4) = 8 + 4 = 12 \][/tex]

### Simplify the First Part
5. Now, work on the first part:
[tex]\[ -12 \div (-4) = 3 \][/tex]
plug it back:
[tex]\[ [-2 + 3] \][/tex]

6. Simplify the addition:
[tex]\[ -2 + 3 = 1 \][/tex]

### Perform the Operations
7. Continue with:
[tex]\[ 1 \times (-6) = -6 \][/tex]

### Combine the Results
8. Finally, add the two parts:
[tex]\[ -6 + 12 = 6 \][/tex]

So, the final result of the given expression is:
[tex]\[ 6 \][/tex]
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