To find the missing step in the proof that 12a + 10 + a = 10 + a + 12a, we can apply the Commutative Property, which states that the order of addition does not affect the sum.
Starting with the left-hand side, we have:
Step 1: 12a + (10 + a)
In this step, we group 10 and a, which can be rearranged because of the Commutative Property.
Then, moving to Step 2: Step 2: 10 + 13a = 10 + 13a
Finally, we can conclude with Step 3: The expressions are equivalent because they both equal the same value.
Now looking at the provided options for Step 1, the closest match to the operation we’ve done is:
12a + 10 + a - a = 10 + a + 12a - a
This shows the equivalence step and uses the element of the Commutative Property by manipulating the expression. However, since none of the options precisely represents our movement towards Step 2 directly by grouping terms, the option most aligned with this reasoning would be:
12a + 10 + a - a = 10 + a + 12a - a.
This choice indicates we're adjusting the expression by removing 'a' from both sides but doesn't straightforwardly indicate grouping.
To summarize, here’s your sequence noted with the logic:
- Step 1: Just rearranging and grouping using the Commutative Property
- Step 2: Understanding how both equal after combining terms.
- Step 3: Final conclusion of equivalence.
The most coherent match is not perfect in the provided answers but closest in spirit to using the Commutative Property as intended.
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