Question

Use the Commutative Property to determine the missing step in proving the equivalence of
.
Step 1: [missing]
Step 2:
Step 3: The expressions are equivalent because they both equal the same value.
(1 point)
12a + 10 + a = 10 + a + 12a
10 + 13a = 10 + 13a
12a + 10 + a − a = 10 + a + 12a − a
10 + 12a + a = 10 + 13a
12a + 10 + a − 10 = 10 + a + 12a − 10
12a + 10 = 10 + 12a

Answer 1

To fill in the missing step using the Commutative Property, we need to rearrange the terms from the first expression to match the second expression.

Here’s how we can structure the proof based on the information given:

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

**Step 2:**
10 + a + 12a = 10 + 13a

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

The missing step utilizes the Commutative Property of Addition, which states that the order in which you add numbers does not change the sum. By rearranging the terms appropriately, we show that the expressions are equal after combining like terms.