To simplify the expression [tex]\( 19 - \{8 + 27 \div (2 \times 8 - 7)\} \)[/tex], we need to follow a series of steps, working from the innermost parentheses to the outermost parts of the expression.
Let's go step by step:
1. Evaluate the expression inside the innermost parentheses:
[tex]\[
2 \times 8 - 7
\][/tex]
First, we'll perform the multiplication:
[tex]\[
2 \times 8 = 16
\][/tex]
Then, subtract 7:
[tex]\[
16 - 7 = 9
\][/tex]
So, [tex]\( 2 \times 8 - 7 \)[/tex] simplifies to 9.
2. Evaluate the division with the result obtained from the parentheses:
[tex]\[
27 \div 9
\][/tex]
Dividing 27 by 9 gives:
[tex]\[
27 \div 9 = 3
\][/tex]
3. Now, evaluate the expression inside the braces:
[tex]\[
8 + 3
\][/tex]
Adding 8 and 3 together gives:
[tex]\[
8 + 3 = 11
\][/tex]
4. Finally, evaluate the outermost expression:
[tex]\[
19 - 11
\][/tex]
Subtracting 11 from 19 gives:
[tex]\[
19 - 11 = 8
\][/tex]
Thus, the simplified result of the given expression [tex]\( 19 - \{8 + 27 \div (2 \times 8 - 7)\} \)[/tex] is [tex]\( 8 \)[/tex].
