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.

12a+10=10+12a

12a+10+a−10=10+a+12a−10

12a+10+a−a=10+a+12a−a

10+12a+a=10+13a

Answer 1

so which answer is it?

Answer 2

To determine the missing step in proving the equivalence of \( 12a + 10 + a = 10 + a + 12a \) using the Commutative Property, we can identify that the missing step involves rearranging the terms on the left side of the equation to match the right side.

Here's the completed proof with the missing step included:

**Step 1: 12a + 10 + a = 10 + 12a + a** (Rearranging the terms using the Commutative Property)

**Step 2: 10 + 12a + a = 10 + 13a** (Combining like terms)

**Step 3: The expressions are equivalent because they both equal the same value.**

So, the missing step is:

**Step 1: 12a + 10 + a = 10 + 12a + a**

This step utilizes the Commutative Property of addition, allowing us to rearrange the terms freely.

Answer 3

The missing step is:

**Step 1: 12a + 10 + a = 10 + 12a + a**

This step uses the **Commutative Property** to rearrange the terms on the left side.