Question

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

10+12a+a=10+13a
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

12a+10=10+12a

Answer 1

To prove the equivalence \( 12a + 10 + a = 10 + a + 12a \) using the Commutative Property, we need to rearrange the terms in the expression.

The correct missing step would be:

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

Now let's rearrange the terms:

Step 2: \( 10 + 12a + a = 10 + a + 12a \) (using the Commutative Property).

This means that the correct missing step to complete the proof would be:

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

However, looking at the provided options, the one that directly correlates with this logic is:

10 + 12a + a = 10 + 13a

So, writing that format eventually summarizes that:

10 + 12a + a = 10 + 13a.

Thus, the answer is: 10 + 12a + a = 10 + 13a.

If your choices need to match exactly to one from your list, it seems the best fit would be:

12a + 10 = 10 + 12a

This represents a symmetry, leading towards the same side of the equation equivalently showing the process of reaching an equivalent fact through switching the placement of the components in the equation.