Let's break down and solve the expression step by step:
1. The expression given is:
[tex]\[ 2 - 4 + 3\left(\sqrt{9} \times 12 - \left(2 + 2^3 \div 2\right) - 1\right) \][/tex]
2. First part: Calculate [tex]\( 2 - 4 \)[/tex]:
[tex]\[ 2 - 4 = -2 \][/tex]
3. Second part: Solve the expression inside the parentheses:
[tex]\[ 3\left(\sqrt{9} \times 12 - \left(2 + 2^3 \div 2\right) - 1\right) \][/tex]
4. Calculate [tex]\( \sqrt{9} \)[/tex]:
[tex]\[ \sqrt{9} = 3 \][/tex]
5. Multiply by 12:
[tex]\[ 3 \times 12 = 36 \][/tex]
6. Evaluate the inner expression [tex]\( 2 + 2^3 \div 2 \)[/tex]:
[tex]\[ 2^3 = 8 \][/tex]
[tex]\[ 8 \div 2 = 4 \][/tex]
[tex]\[ 2 + 4 = 6 \][/tex]
7. Substitute the evaluated parts back into the main expression:
[tex]\[ 3\left(36 - 6 - 1\right) \][/tex]
8. Simplify [tex]\( 36 - 6 - 1 \)[/tex]:
[tex]\[ 36 - 6 = 30 \][/tex]
[tex]\[ 30 - 1 = 29 \][/tex]
9. Now multiply by 3:
[tex]\[ 3 \times 29 = 87 \][/tex]
10. Summing up the result from the two main parts:
[tex]\[ -2 + 87 = 85 \][/tex]
Therefore, the final result of the entire expression is:
[tex]\[ 85 \][/tex]
