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

12a+10+a−a=10+a+12a−a

10+12a+a=10+13a

12a+10=10+12a

Answer 1

Just choose a, b, c, or d

Answer 2

To determine the missing step using the Commutative Property, we need to rearrange the terms in the expression on the left side of the equation.

The original expression is: \( 12a + 10 + a \)

We want to rewrite this expression such that it matches \( 10 + a + 12a \).

The correct missing step would be:

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

So the missing step that uses the Commutative Property is:

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

Thus, the best response from the options provided is:

**10 + 12a + a = 10 + 13a** (but note that the direct application of the Commutative Property isn't exactly captured by the choices given).

However, based on the simplified alternatives, we can say that the missing step in context is:

**12a + 10 + a = 10 + a + 12a** (implicitly applying the Commutative Property).

If you need to choose from the options you have:
**12a+10+a−10=10+a+12a−10** is also incorrect as it doesn't apply the property cleanly.

Thus, internal steps that made sense in this context might not be explicitly listed in the multiple-choice format. The closest matches would help to clarify for further learning exercises on similar properties.

Answer 3

The correct response is:

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