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+a−a=10+a+12a−a
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

Answer 1

To prove the equivalence of \( 12a + 10 + a \) and \( 10 + a + 12a \) using the Commutative Property, we need to rearrange the terms in the first expression to match the second expression. The second step shows that both expressions simplify to \( 10 + 13a \).

The missing step in the proof can be written as:

Step 1: \( 12a + 10 + a = 10 + 12a + a \)

Using the Commutative Property, we can rearrange the terms:

We see that when we combine like terms, we can also rearrange the expressions, which leads us to:

After simplification, we have:

Step 2: \( 10 + 13a = 10 + 13a \)

So, the correct response would be:

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

To confirm, this step effectively utilizes the Commutative Property to rearrange the terms.