Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a .

Question

Step 1: [missing]

Step 2: 10+13a=10+13a

Step 3: The expressions are equivalent because they both equal the same value.

(1 point)
Responses

12a+10=10+12a
d plus 10 plus a equals 10 plus a plus d

12a+10+a−a=10+a+12a−a
d plus 10 plus a equals 10 plus a plus d

12a+10+a−10=10+a+12a−10
d plus 10 plus a equals 10 plus a plus d

10+12a+a=10+13a
d plus 10 plus a equals 10 plus a plus d
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Answer 1

To determine the missing step in the proof of equivalence between \( 12a + 10 + a \) and \( 10 + a + 12a \) using the Commutative Property, we need to show how we can rearrange the terms.

The expression \( 12a + 10 + a \) can be rearranged as follows:

1. Step 1: 10 + 12a + a = 10 + a + 12a

This rearrangement is valid by the Commutative Property, which states that the order of the terms can be changed in addition.

Now we can conclude:

• Step 2: The equation can also be written as \( 10 + 13a = 10 + 13a \) through combining like terms \( 12a + a = 13a \).

• Step 3: Finally, since both expressions evaluate to the same form, we can state they are equivalent.

Therefore, the correct response for the missing step is:

10 + 12a + a = 10 + a + 12a