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+13astep 3: the expressions are equivalent because they both equal the same value.(1 point)responses12a+10=10+12ad plus 10 plus a equals 10 plus a plus d10+12a+a=10+13ad plus 10 plus a equals 10 plus a plus d12a+10+a−a=10+a+12a−ad plus 10 plus a equals 10 plus a plus d12a+10+a−10=10+a+12a−10

Answer 1

To determine the missing step using the commutative property, we need to rearrange the terms in the expression, which states that the order of addition does not affect the sum.

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

The expression can also be rearranged as \(10 + a + 12a\) (keeping \(10\) and \(a\) first).

Thus, the complete proof would be:

**Step 1:** 12a + 10 + a = 10 + 12a + a
**Step 2:** 10 + 13a = 10 + 13a
**Step 3:** The expressions are equivalent because they both equal the same value.

To clarify the options you provided, the correct missing step is:

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