To simplify the expression [tex]\(4[7 + 6(8 - 5)]\)[/tex], we need to follow the order of operations (PEMDAS/BODMAS), which stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (left to right), and Addition and Subtraction (left to right).
Step-by-Step Solution:
1. Simplify the expression inside the innermost parentheses:
[tex]\[
8 - 5
\][/tex]
This simplifies to:
[tex]\[
3
\][/tex]
2. Next, simplify the expression inside the brackets:
[tex]\[
7 + 6 \times 3
\][/tex]
First, perform the multiplication:
[tex]\[
6 \times 3 = 18
\][/tex]
Now add 7 to the result:
[tex]\[
7 + 18 = 25
\][/tex]
3. Now, multiply the result by 4:
[tex]\[
4 \times 25 = 100
\][/tex]
Thus, the simplified value of the expression [tex]\(4[7 + 6(8 - 5)]\)[/tex] is:
[tex]\[
\boxed{100}
\][/tex]
