To simplify the expression [tex]\(18 + 2[\{9 - 2(27 \div 3 - 5) + 4\} + 2]\)[/tex], follow these step-by-step instructions:
1. Inner Division:
First, simplify the division inside the parentheses:
[tex]\[
27 \div 3 = 9
\][/tex]
2. Subtraction:
Next, subtract 5 from the result:
[tex]\[
9 - 5 = 4
\][/tex]
3. Multiplication:
Now, multiply this result by 2:
[tex]\[
2 \cdot 4 = 8
\][/tex]
4. Inner Subtraction:
Subtract this result from 9:
[tex]\[
9 - 8 = 1
\][/tex]
5. Addition within braces:
Add 4 to the result inside the inner braces:
[tex]\[
1 + 4 = 5
\][/tex]
6. Addition:
Now, handle the term [tex]\(\{5 + 2\}\)[/tex]:
[tex]\[
5 + 2 = 7
\][/tex]
7. Multiplication by 2:
Multiply this result by 2:
[tex]\[
2 \cdot 7 = 14
\][/tex]
8. Final Addition:
Finally, add 18 to the result:
[tex]\[
18 + 14 = 32
\][/tex]
The simplified value of the expression [tex]\(18 + 2[\{9 - 2(27 \div 3 - 5) + 4\} + 2]\)[/tex] is:
[tex]\[
\boxed{32}
\][/tex]
