To identify which step contains the mistake in the given expression simplification, let’s go through the steps one by one.
The original expression is:
[tex]\[
\frac{9}{2} + 3(4-1) - 7 + 2^3
\][/tex]
Step 1: Evaluate the expression inside the parentheses (4-1) and the power [tex]\( 2^3 \)[/tex]:
[tex]\[
= \frac{9}{2} + 3(3) - 7 + 8
\][/tex]
Step 1 is correct.
Step 2: Perform the multiplication [tex]\(3(3)\)[/tex] and keep evaluating [tex]\(2^3 = 8\)[/tex]:
[tex]\[
= \frac{9}{2} + 9 - 7 + 8
\][/tex]
Step 2 is correct.
Step 3: Here, we need to check the correctness. At this step, we should just continue adding and subtracting left to right:
The given Step 3 is:
[tex]\[
= \frac{15}{2} (3) - 7 + 8
\][/tex]
This is incorrect because the [tex]\(\frac{9}{2}\)[/tex] should not be multiplied by 3. Instead, we should sum and subtract the terms as they are:
Let's correct this step:
[tex]\[
= \frac{9}{2} + 9 - 7 + 8
\][/tex]
Step 4: Combine the terms left to right correctly:
For correct calculation:
[tex]\[
\frac{9}{2} = 4.5 \implies 4.5 + 9 - 7 + 8
\][/tex]
[tex]\[
= 4.5 + 9 = 13.5\][/tex]
\]
[tex]\[
= 13.5 - 7 = 6.5
\][/tex]
[tex]\[
= 6.5 + 8 = 14.5
\][/tex]
Our correct result should be [tex]\(\frac{29}{2} (= 14.5)\)[/tex]. But in the given incorrect simplification:
\[
= \frac{45}{2} - 7 + 8
This implies \[ Step 3. Step 3 should not include multiplication
So, the mistake is in Step 3.
The correct expression without mistakes is:
\(\result {29}{2}\}.
Therefore, the correct answer choice is:
C. Step 3
