Let's solve the expression step-by-step and identify where the mistake occurs.
The given expression is:
[tex]\[
\frac{9}{2} + 3(4-1) - 7 + 2^3
\][/tex]
Step 1: Simplify inside the parentheses and calculate the exponent.
[tex]\[
4 - 1 = 3 \quad \text{and} \quad 2^3 = 8
\][/tex]
So we get:
[tex]\[
\frac{9}{2} + 3(3) - 7 + 8
\][/tex]
Step 2: Perform the multiplication.
[tex]\[
3(3) = 9
\][/tex]
This gives:
[tex]\[
\frac{9}{2} + 9 - 7 + 8
\][/tex]
Step 3: Perform the additions and subtractions from left to right.
First, calculate [tex]\(\frac{9}{2}\)[/tex]:
[tex]\[
\frac{9}{2} = 4.5
\][/tex]
Now simplify the expression step by step:
[tex]\[
4.5 + 9 = 13.5
\][/tex]
[tex]\[
13.5 - 7 = 6.5
\][/tex]
[tex]\[
6.5 + 8 = 14.5
\][/tex]
However, the given solutions state that the result should be:
[tex]\[
3
\][/tex]
Clearly, the calculations indicate an inconsistency between the steps initially provided in the question and the correct calculations.
Step-by-Step Analysis of Provided Steps:
- Step 1: Correctly applies parentheses and exponent rules.
- Step 2: Correctly performs multiplication.
- Step 3: Here the term [tex]\(\frac{15}{2} (3)\)[/tex] is introduced, which seems incorrect. It should retain the terms as separated by addition or subtraction.
- Step 4, 5, and 6: These are continuation of Step 3's mistake.
Thus, the mistake occurs in:
[tex]\[
\text{Step 3: } = \frac{15}{2} (3) - 7 + 8
\][/tex]
Correct Answer:
A. Step 3
