Let's carefully examine each step:
[tex]\[
\frac{1+3^2}{5}+|-10| \div 2
\][/tex]
Step 1:
[tex]\[
=\frac{1+3^2}{5}+10 \div 2
\][/tex]
This step correctly simplified [tex]\(|-10|\)[/tex] to [tex]\(10\)[/tex], so no mistake here.
Step 2:
[tex]\[
=\frac{1+9}{5}+10 \div 2
\][/tex]
This step correctly evaluated [tex]\(3^2\)[/tex] as [tex]\(9\)[/tex], no mistake here either.
Step 3:
[tex]\[
=\frac{10}{5}+10 \div 2
\][/tex]
This correctly adds [tex]\(1 + 9\)[/tex] to [tex]\(10\)[/tex], so still no mistake.
Step 4:
[tex]\[
=2+10 \div 2
\][/tex]
[tex]\(\frac{10}{5}\)[/tex] is correctly evaluated to [tex]\(2\)[/tex]. However, we need to be careful because this step contains an addition and a division operation.
In PEMDAS/BODMAS rules, division should be performed before addition. So, we should first divide the [tex]\(10 \div 2\)[/tex] and then add [tex]\(2\)[/tex].
Let's rewrite it properly:
[tex]\[
2 + \left(10 \div 2\right)
\][/tex]
This equals:
[tex]\[
2 + 5
\][/tex]
Which leads to:
Step 5:
[tex]\[
=2+5
\][/tex]
Step 6:
[tex]\[
=7
\][/tex]
So the correct simplification should result in [tex]\(7\)[/tex], but in the given steps:
Step 5:
[tex]\[
=12 \div 2
\][/tex]
This step incorrectly adds [tex]\(2 + 10\)[/tex] and then divides by [tex]\(2\)[/tex].
Thus, the mistake occurred in Step 5, since it did not adhere to the proper order of operations, which dictates that division should be carried out before addition.
The correct answer here is B. Step 5.
