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−a=10+a+12a−a
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=10+12a
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, we need to use the Commutative Property of Addition, which states that changing the order of addends does not change the sum.

Given the expressions, we want to transform \( 12a + 10 + a \) into \( 10 + a + 12a \).

So, the appropriate missing step would be:

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

This uses the Commutative Property to rearrange the terms to match the format needed for Step 2.

Thus, the correct completion of the proof would look like this:

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

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

Step 3: The expressions are equivalent because they both equal the same value.