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=10+12a
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

10+12a+a=10+13a
d plus 10 plus a equals 10 plus a plus d

12a+10+a−a=10+a+12a−a

Answer 1

To determine the missing step in proving the equivalence of \( 12a + 10 + a = 10 + a + 12a \) using the Commutative Property, we need to rearrange the terms on the left side so that they match the right side.

The left side \( 12a + 10 + a \) can be rearranged to \( 10 + a + 12a \) by first applying the Commutative Property.

Thus, the missing step should be:

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

In this case, you can group the \( 12a \) and \( a \) together. So, the correct missing response is:

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

However, since this option doesn't exist directly, the correct logical choice is:

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

which is a valid application of the Associative and Commutative properties combined, but it doesn't seem explicitly listed.

Among the given options, the correct missing step most closely represented is:

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

This option correctly illustrates that you can rearrange and combine like terms to simplify the expression to achieve step 2.

So, my conclusion regarding the missing step would be:

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