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

12a+10+a−a=10+a+12a−a
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

Answer 1

The missing step in proving the equivalence of \( 12a + 10 + a = 10 + a + 12a \) using the Commutative Property is:

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

This step simply rearranges the terms on the left side of the equation.

So the complete proof would look like this:

1. \( 12a + 10 + a = 10 + 12a + a \) (using the Commutative Property)
2. \( 10 + 13a = 10 + 13a \) (by combining like terms)
3. The expressions are equivalent because they both equal the same value.

Therefore, the correct response is: 12a + 10 = 10 + 12a.