Let's solve the expression step-by-step.
The expression to evaluate is:
[tex]\[12 \times\{-5+(-2)[9-6(15-24)]\}\][/tex]
1. Innermost Parentheses:
Start by evaluating the innermost expression within the parentheses:
[tex]\[
15 - 24 = -9
\][/tex]
2. Inside the Square Brackets:
Next, substitute [tex]\(-9\)[/tex] back into the expression within the square brackets:
[tex]\[
9 - 6(-9)
\][/tex]
Now, multiply [tex]\( -6 \)[/tex] by [tex]\(-9\)[/tex]:
[tex]\[
-6 \times (-9) = 54
\][/tex]
So, the expression inside the brackets becomes:
[tex]\[
9 + 54 = 63
\][/tex]
3. Inside the Braces:
Replace the computed value [tex]\( 63 \)[/tex] into the expression with the braces:
[tex]\[
-5 + (-2)[63]
\][/tex]
Then, multiply [tex]\( -2 \)[/tex] by [tex]\( 63 \)[/tex]:
[tex]\[
-2 \times 63 = -126
\][/tex]
Now add [tex]\( -126 \)[/tex] to [tex]\( -5 \)[/tex]:
[tex]\[
-5 - 126 = -131
\][/tex]
4. Final Multiplication:
Lastly, multiply the value inside the braces by 12:
[tex]\[
12 \times (-131) = -1572
\][/tex]
Therefore, the result of the expression is:
[tex]\[ \boxed{-1572} \][/tex]
