We must identify any errors in Arlene's work. We will see that the only mistake there is that she confuses the commutative property with the associative.
We start with the sum:
−7.9 + 8.2 − 3.4 + 2.1
First she rewrites it as:
−7.9 + 8.2 + (− 3.4) + 2.1
Nothing wrong here.
Now she applies the associative property, which tells us that we can perform the sum in any order we want, but she does it to commute the terms to:
−7.9 + (− 3.4) + 8.2 + 2.1
So here it should say "commutative property" instead of associative.
Then, in the next step, she actually applies the associative property, but this time it says "commutative", so it is also wrong.
(−7.9 + (− 3.4)) + (8.2 + 2.1)
Then she simplifies to:
-11.3 + 10.3 = -1
So the only error in her work is that she mixes the associative property which says that:
A + B + C = (A + B) + C = A + (B + C)
With the commutative property, which says that:
A + B = B + A
If you want to learn more about adition properties, you can read:
https://brainly.com/question/2475734
