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

To determine the missing step in the proof, we need to consider the Commutative Property, which states that the order of addition does not affect the sum.

Given the expression \(12a + 10 + a\) and wanting to show that it is equivalent to \(10 + a + 12a\), let's analyze what the expressions look like in terms of reordering the terms.

Starting with Step 2:
- We see that \(10 + 13a\) is the simplified version of \(12a + 10 + a\) since \(12a + a = 13a\).

The missing step should rearrange \(12a + 10 + a\) to match the target expression \(10 + a + 12a\) before simplifying.

Looking at the options provided:

A. \(10 + 12a + a = 10 + 13a\) - This is a valid rearrangement, but it doesn't match the format we are looking for since we want to move \(12a\) to the back.

B. \(12a + 10 + a - 10 = 10 + a + 12a - 10\) - This involves subtraction which complicates the proof without need.

C. \(12a + 10 + a - a = 10 + a + 12a - a\) - This also complicates things unnecessarily with subtraction.

D. \(12a + 10 = 10 + 12a\) - This uses the Commutative Property directly on part of the expression and correctly rearranges the terms, but it’s not the whole expression yet.

While options A and D are close, option A provides the necessary transition directly to the setup for simplification followed by comparison.

Therefore, the missing step is:

**A. \(10 + 12a + a = 10 + 13a\)**