Question

The following expression has been simplified one step at a time. Match each step with the property used to get to that step. (Note: The column that lists the algebraic expressions is already in the correct order.)

1. (3 + 6x) - 5x
2. 3 + (6x - 5x)
3. 3 + (6 - 5) x
4. 3 + (1) x
5. 3 + x

a. multiplicative identity
b. distributive
c. associative
d. subtraction
e. commutative

Answer 1

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)