Sure, let's solve the given expression step-by-step:
The expression to solve is:
[tex]\[
\{[18+(15-7) \times 2] \div 17\}+\{52-3(42-15)\}
\][/tex]
### Step-by-Step Solution:
1. Simplify the expression inside the first set of square brackets:
[tex]\[
15 - 7 = 8
\][/tex]
2. Now, substitute this result back into the expression:
[tex]\[
18 + 8 \times 2
\][/tex]
3. Perform the multiplication inside the square brackets:
[tex]\[
8 \times 2 = 16
\][/tex]
4. Add the result of the multiplication to 18:
[tex]\[
18 + 16 = 34
\][/tex]
5. Now, divide by 17:
[tex]\[
34 \div 17 = 2.0
\][/tex]
6. Next, simplify the expression inside the second set of curly braces:
[tex]\[
42 - 15 = 27
\][/tex]
7. Now, substitute this result back into the expression inside the curly braces:
[tex]\[
52 - 3 \times 27
\][/tex]
8. Perform the multiplication inside the curly braces:
[tex]\[
3 \times 27 = 81
\][/tex]
9. Subtract the result of the multiplication from 52:
[tex]\[
52 - 81 = -29
\][/tex]
10. Finally, add the results from both parts:
[tex]\[
2.0 + (-29) = -27.0
\][/tex]
So, the final result of the expression [tex]\(\{[18+(15-7) \times 2] \div 17\}+\{52-3(42-15)\}\)[/tex] is:
[tex]\[
-27.0
\][/tex]
