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+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

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

Answer 1

To complete the proof using the Commutative Property, we want to rearrange the terms in the expression \(12a + 10 + a\) such that it matches the form \(10 + a + 12a\).

Step 1 should be:

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

This follows from the Commutative Property, which allows us to change the order of addition.

So, the response that best matches this is:

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

Thus, after step 1, we can proceed to combine like terms in Step 2 to reach the equality shown.

The final answer for the missing step would be:

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