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

Answer 1

To determine the missing step in proving the equivalence of \(12a + 10 + a = 10 + a + 12a\), we can apply the Commutative Property, which states that the order of addition can be changed without affecting the sum.

We start with the left-hand side of the equation:

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

   • (This step uses the Commutative Property to rearrange terms.)

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

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

So, the missing step is \( 12a + 10 + a = 10 + 12a + a \). This reflects the use of the Commutative Property.