Question

Use the commuter probably to determine the missing step in proving the equivalent of 12a + 10 + a = 10 + a + 12a step 1 is missing step 2 10 + 13A = 10 + 13A step 3 the expressions are equivalent because they both equal the same

Answer 1

To prove that the expressions \( 12a + 10 + a \) and \( 10 + a + 12a \) are equivalent, we can identify the missing step between step 1 and step 2.

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

To simplify \( 12a + 10 + a \), we combine like terms. The terms \( 12a \) and \( a \) can be combined:

\[
12a + a = 13a
\]

So, we can rewrite Step 1:

**Step 1 (completed):** \( 12a + 10 + a = 13a + 10 \)

Now we can proceed to step 2, confirming the equivalence:

**Step 2 (as given):** \( 10 + 13a \)

This is the same as \( 13a + 10 \) since addition is commutative.

**Step 3:** The expressions \( 13a + 10 \) and \( 10 + 13a \) are equivalent because they both equal the same thing.

Therefore, the missing step is the simplification of \( 12a + 10 + a \) into \( 13a + 10 \).