Let's go through each step to identify the mistake:
Original Expression:
[tex]\[
\frac{1 + 3^2}{5} + |-10| \div 2
\][/tex]
Step 1:
[tex]\[
\frac{1 + 3^2}{5} + 10 \div 2
\][/tex]
This step is correct because:
[tex]\[
3^2 = 9 \quad \text{and} \quad |-10| = 10
\][/tex]
Step 2:
[tex]\[
\frac{1 + 9}{5} + 10 \div 2
\][/tex]
This step is also correct since we replaced [tex]\(3^2\)[/tex] with 9:
[tex]\[
1 + 9 = 10
\][/tex]
Step 3:
[tex]\[
\frac{10}{5} + 10 \div 2
\][/tex]
Again, this step is correct as [tex]\(1 + 9 = 10\)[/tex]:
[tex]\[
\frac{10}{5} = 2
\][/tex]
Step 4:
[tex]\[
2 + 10 \div 2
\][/tex]
This step is accurate as the fraction [tex]\( \frac{10}{5} \)[/tex] was simplified to 2.
Now let's look closely at Step 5:
[tex]\[
12 \div 2
\][/tex]
This step is incorrect. In Step 4, we have:
[tex]\[
2 + \frac{10}{2} = 2 + 5 = 7
\][/tex]
Instead, what should have been written is:
[tex]\[
2 + 5 = 7
\][/tex]
The correct final result should be:
[tex]\[
7
\][/tex]
Therefore, Step 5 is where the error occurred.
Correct Answer:
A. Step 5
