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 10+12a+a=10+13a 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

Answer 1

To determine the missing step in the proof that shows the equivalence of \(12a + 10 + a\) and \(10 + a + 12a\) using the Commutative Property, let's first rewrite the original expression:

1. Start with \(12a + 10 + a\).

Using the Commutative Property, we can change the order of addition. The missing step should reflect an arrangement where we can simplify the left-hand side:

The correct missing step should be:

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

So the entire proof would look like this:

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

Thus, the correct response is:

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