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 d plus 10 plus a equals 10 plus a plus d

Answer 1

To determine the missing step in your proof, we need to apply the Commutative Property to rearrange the terms.

The expression we start with is \(12a + 10 + a\). We can rearrange the terms using the Commutative Property of Addition, which states that changing the order of addends does not change the sum.

Therefore, the missing step should be:

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

After this step, you can combine \(12a + a\) to get \(13a\), leading to:

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

Finally, you conclude that the expressions are equivalent because they both equal the same value.

So, the answer would be:

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