Question

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+a−10=10+a+12a−10


12a+10+a−a=10+a+12a−a


12a+10=10+12a


10+12a+a=10+13a

Answer 1

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.