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