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Simplify:

a. [tex]18+2\left[\{9-2\left(\frac{27}{3}-5\right)+4\}+2\right][/tex]


Sagot :

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]
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