To identify where the mistake occurs, let's carefully go through the initial simplification of the given expression step-by-step:
Given expression:
[tex]\[ \frac{9}{2} + 3(4 - 1) - 7 + 2^3 \][/tex]
Step 1:
[tex]\[ \frac{9}{2} + 3(3) - 7 + 2^3 \][/tex]
In this step, the expression inside the parentheses [tex]\((4 - 1)\)[/tex] is correctly calculated as 3.
Step 2:
[tex]\[ \frac{9}{2} + 3(3) - 7 + 8 \][/tex]
Here, [tex]\(2^3\)[/tex] is correctly evaluated as 8, so this step is correctly done assuming the steps follow proper order.
Step 3:
[tex]\[ \frac{15}{2} (3) - 7 + 8 \][/tex]
In this step, it appears an error is made. The term [tex]\(\frac{9}{2}\)[/tex] should remain as [tex]\(\frac{9}{2}\)[/tex], and [tex]\(3(3)\)[/tex] should give 9, not 3. Moreover, it seems there is an attempt to distribute multiplication incorrectly which is not supposed to happen.
The correct continuation from Step 2 should have been:
[tex]\[ \frac{9}{2} + 9 - 7 + 8 \][/tex]
Therefore, the mistake is in Step 3, where the multiplication and division were incorrectly applied.
So, the correct answer is:
C. Step 3
