Sure, let's solve the given expression step by step.
The given expression is:
[tex]\[ \left( [-2 + \left( \frac{-12}{-4} \right)] \times (-6) \right) + \left\{ 8 - \left[ 11 - \left( \frac{9+1}{-2} \right) \right] \div (-4) \right\} \][/tex]
We will start by solving the innermost expressions.
1. First, solve the division inside the square brackets and curly braces:
[tex]\[ \frac{-12}{-4} = 3 \][/tex]
[tex]\[ 9 + 1 = 10 \][/tex]
[tex]\[ \frac{10}{-2} = -5 \][/tex]
2. Substitute these values back into the expression:
[tex]\[ \left( [-2 + 3] \times (-6) \right) + \left\{ 8 - \left[ 11 - (-5) \right] \div (-4) \right\} \][/tex]
3. Now, solve the expressions inside the brackets and curly braces:
[tex]\[ -2 + 3 = 1 \][/tex]
[tex]\[ 11 - (-5) = 11 + 5 = 16 \][/tex]
4. Substitute these values back into the expression:
[tex]\[ \left( [1] \times (-6) \right) + \left\{ 8 - \left( 16 \div (-4) \right) \right\} \][/tex]
5. Continue solving inside the curly braces:
[tex]\[ 16 \div (-4) = -4 \][/tex]
6. Substitute this value back into the expression:
[tex]\[ \left( 1 \times (-6) \right) + \left\{ 8 - (-4) \right\} \][/tex]
7. Calculate the final expression inside the curly braces:
[tex]\[ 8 - (-4) = 8 + 4 = 12 \][/tex]
8. Now, solve the multiplication and the outer addition:
[tex]\[ 1 \times (-6) = -6 \][/tex]
[tex]\[ -6 + 12 = 6 \][/tex]
So, the final result of the given expression is [tex]\( 6 \)[/tex].
