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

12a+10+a−10=10+a+12a−10

1 answer

To determine the missing step in proving the equivalence of \( 12a+10+a=10+a+12a \) using the Commutative Property, we can rearrange the terms appropriately.

Let's break it down:

The goal is to express \( 12a + 10 + a \) in a way that highlights its equivalence to \( 10 + a + 12a \).

In Step 1, we can rearrange the terms:

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

This matches the structure leading to Step 2. From Step 1, we can combine like terms (the \( 12a + a = 13a \)), giving us:

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

Thus, the complete sequence is:

  • Step 1: \( 10 + 12a + a = 10 + a + 12a \)
  • Step 2: \( 10 + 13a = 10 + 13a \)
  • Step 3: The expressions are equivalent because they both equal the same value.

Of the options provided, the correct missing step is:

10 + 12a + a = 10 + a + 12a.