Let's review each step in detail to locate the mistake.
Given expression:
[tex]\[
\frac{9}{2} + 3(4-1) - 7 + 2^3
\][/tex]
Step 1:
[tex]\[
\frac{9}{2} + 3(4-1) - 7 + 2^3 = \frac{9}{2} + 3(3) - 7 + 2^3
\][/tex]
This step looks correct, where [tex]\(4 - 1 = 3\)[/tex].
Step 2:
[tex]\[
\frac{9}{2} + 3(3) - 7 + 2^3 = \frac{9}{2} + 3(3) - 7 + 8
\][/tex]
This step is also correct because [tex]\(2^3 = 8\)[/tex].
Step 3:
[tex]\[
\frac{9}{2} + 3(3) - 7 + 8 = \frac{15}{2}(3) - 7 + 8
\][/tex]
This step is incorrect. The correct simplification of [tex]\(\frac{9}{2} + 3(3) - 7 + 8\)[/tex] should be:
[tex]\[
\frac{9}{2} + 9 - 7 + 8
\][/tex]
Clearly, a simplification error was introduced here. Let's verify this by double-checking the correct sequence of steps:
Correct intermediate step:
[tex]\[
\frac{9}{2} + 9 - 7 + 8
\][/tex]
So, the answer is:
The mistake occurs in Step 3.
Therefore, the correct answer is:
C. Step 3
