When we want to identify properties, we first need to know what each of the properties do. Let's review.
Property
Meaning
Example
Commutative Property of Addition
The order of addition does not change the outcome
5 + 6 = 6 + 5
Additive Inverse Property
Pairs of numbers add to be zero
5 + (-5) = 0
Additive Identity Property
When we add zero to a number, it does not change the number
9 + 0 = 9
Associative Property of Addition
We can change which numbers we choose to add first.
5 + (4 + 6) = (5 + 4) + 6
Our expression, 2x+0=2x, has a zero in it. So it's either the inverse property or the identity property. Since there is no negative in it, it must be NOT be the inverse property. Therefore, it represents the Additive Identity property, choice C.
