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=10+12a
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+a−10=10+a+12a−10
d plus 10 plus a equals 10 plus a plus d
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Answer 1

To complete the proof using the Commutative Property, we want to rearrange the terms in the expression \(12a + 10 + a\) so that it matches the order in the expression \(10 + a + 12a\).

The correct missing step is:

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

This rearrangement applies the Commutative Property, which states that the order of addition does not affect the sum.

So the complete sequence would be:

Step 1: \(12a + a + 10 = 10 + a + 12a\)
Step 2: \(10 + 13a = 10 + 13a\)
Step 3: The expressions are equivalent because they both equal the same value.