Final answer:
The simplification of the expression (3 + 6x) - 5x involves applying the associative property, commutative property, and subtraction to reorganize and combine like terms, and the multiplicative identity to simplify the multiplication by one.
Step-by-step explanation:
The given expression (3 + 6x) - 5x has been simplified one step at a time, and we need to match each step with the property used to reach that step:
(3 + 6x) - 5x
3 + (6x - 5x)
3 + (6 - 5) x
3 + (1) x
3 + x
The properties matched to each step are as follows:
From step 1 to step 2, we use the associative property of addition to regroup the terms.
From step 2 to step 3, we apply the commutative property of addition within the parentheses to simplify the like terms.
From step 3 to step 4, the subtraction operation is used to combine the like terms (6 - 5).
From step 4 to step 5, we apply the multiplicative identity to remove the unnecessary multiplication by 1 (1x = x).
Therefore, the correct matching is:
c. associative
e. commutative
d. subtraction
a. multiplicative identity
(No property is mentioned from step 4 to step 5 as it's a result of multiplicative identity already applied in the previous step)