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
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

Answer 1

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 + a**

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.