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=10+12a
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

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

10+12a+a=10+13a

Answer 1

To find the missing step in the proof of the equivalence of \( 12a + 10 + a = 10 + a + 12a \), we can identify the appropriate expression that uses the Commutative Property.

The Commutative Property states that the order in which two numbers are added does not change the sum. Therefore, we can rearrange the terms.

The first step can be to rearrange the terms on the left side of the equation:

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

Now, when we combine \( 12a + a \) on the left side, we have:

**Step 2**: \( 10 + 13a = 10 + 13a \)

Thus, the missing step in proving the equivalence is:

**Response**: \( 12a + a + 10 = 10 + a + 12a \)