Certainly! Let's simplify the given expression step-by-step: [tex]\( 45 \times 2 + 3[660 \div 3 \{6 + 8(12 - 7) - 3\}] \)[/tex].
1. First, start simplifying the innermost parentheses: [tex]\( (12 - 7) \)[/tex].
[tex]\[
12 - 7 = 5
\][/tex]
2. Next, substitute this result into the expression inside the curly braces: [tex]\( 6 + 8(5) - 3 \)[/tex].
[tex]\[
6 + 8 \times 5 - 3
\][/tex]
Multiply inside the parentheses first: [tex]\( 8 \times 5 \)[/tex].
[tex]\[
8 \times 5 = 40
\][/tex]
So, we now have:
[tex]\[
6 + 40 - 3
\][/tex]
Perform the addition and subtraction:
[tex]\[
6 + 40 - 3 = 43
\][/tex]
3. After simplifying the expression inside the curly braces, we substitute this result into the square brackets: [tex]\( 660 \div 3 \div 43 \)[/tex].
[tex]\[
660 \div 3 = 220
\][/tex]
Now perform the division:
[tex]\[
220 \div 43 \approx 5.1163
\][/tex]
4. Next, substitute this result into the main expression: [tex]\( 45 \times 2 + 3 \times 5.1163 \)[/tex].
[tex]\[
45 \times 2 = 90
\][/tex]
Then multiply:
[tex]\[
3 \times 5.1163 \approx 15.3489
\][/tex]
Finally, add these results together:
[tex]\[
90 + 15.3489 \approx 105.3489
\][/tex]
Thus, the simplified value of the expression [tex]\( 45 \times 2 + 3[660 \div 3 \{6 + 8(12 - 7) - 3\}] \)[/tex] is approximately [tex]\( 105.3489 \)[/tex].
