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

10+12a+a=10+13a

12a+10+a−a=10+a+12a−a

12a+10=10+12a

Answer 1

To use the Commutative Property to determine the missing step in the proof, we need to rearrange the terms in the expression \(12a + 10 + a\) so that it matches the format of \(10 + a + 12a\). The correct missing step should show the rearrangement of the terms.

The missing step is:

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

This step ensures that all the terms are rearranged to isolate the like terms consistently.

The full proof would look like this:

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.

So, the response you should choose is:

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