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
d plus 10 plus a equals 10 plus a plus d

12a+10=10+12a
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−a=10+a+12a−a

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

To find the missing step using the Commutative Property, we need to reorder the terms in the expression so that it mirrors the right side of the equation (10 + a + 12a). The correct step that satisfies this is:

**Step 1: 12a + 10 + a = 10 + 12a +

This maintains equality while applying the Commutative Property by rearranging the terms. However, to simplify things further after that, you could also combine terms:

**Step 1: 10 + 12a + a = 10 + 13a**

Then you would reach Step 2, which is:

**Step 2: 10 + 13a = 10 + 13a**

So, among the provided options, the following choice accurately reflects the use of the Commutative Property to equate the two expressions:

**10 + 12a + a = 10 + 13a**

However, this exact option is not provided among the choices directly.

If I must select one of the provided answers, then the option that closely resembles a logical middle step would be:

**10 + 12a + a = 10 + 13a** (Although this specific equation is not given, recognizing the form should assist understanding.)

If you're searching for a direct answer, I don't have a perfect match among the options you listed to pinpoint as the missing step, but remember the idea is to adequately utilize the Commutative Property while combining the like terms.