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−a=10+a+12a−a
12a+10+a−10=10+a+12a−10
10+12a+a=10+13a

Answer 1

To determine the missing step in proving the equivalence of \( 12a + 10 + a = 10 + a + 12a \), we can begin from an earlier equation and apply the Commutative Property of Addition, which allows us to rearrange terms in an expression.

Let's rewrite the steps leading up to step 2, focusing on what the missing step would be.

Starting from the left side, we have:
1. \( 12a + 10 + a \)

In this expression, we can rearrange the terms to match the right side:
- By applying the Commutative Property, we can switch the order of \( 10 \) and \( 12a \), and we can also rearrange \( a \) within that context.

So, we can write step 1 as:
**Step 1:** \( a + 12a + 10 \) (using the Commutative Property)

Now continuing to Step 2 from this rearranged form:
2. \( a + 12a + 10 = 10 + a + 12a \) (which we can rearrange as \( 10 + 13a \))

Thus, the full series of steps, with the missing step filled in, would be:
1. **Step 1:** \( a + 12a + 10 \)
2. **Step 2:** \( 10 + 13a = 10 + 13a \)
3. The expressions are equivalent because they both equal the same value.

In summary, the missing step utilizes the Commutative Property to rearrange the terms effectively.