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. (1 point) Responses 12a+10=10+12a d plus 10 plus a equals 10 plus a plus d 10+12a+a=10+13a d plus 10 plus a equals 10 plus a plus d 12a+10+a−10=10+a+12a−10 d plus 10 plus a equals 10 plus a plus d 12a+10+a−a=10+a+12a−a

Answer 1

To determine the missing step in the proof of the equivalence of the expressions \(12a + 10 + a\) and \(10 + a + 12a\) using the Commutative Property, we need to rewrite the first expression to rearrange the terms.

The correct missing step would be:

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

This step rearranges the terms, placing the \(10\) first, followed by \(12a\) and \(a\) together, which leads into the next step you provided.

So the complete reasoning is:

- Step 1: \(12a + 10 + a = 10 + 12a + a\) (rearranging 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.

Therefore, the complete sequence holds true under the Commutative Property.