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)

12a + 10 + a - 10= 10 + a + 12a -10

10 + 12a + a = 10 + 13a

12a + 10 = 10 + 12a

12a + 10 +a - a + 10 + a + 12a - a

Answer 1

Substituting 1 for x in the equation 5x + 3= x * 5 + 3 is a test case for which property?
(1 point)

the associative property of multiplication

the associative property of addition

the commutative property of addition

the commutative property of multiplication

Answer 2

To demonstrate the use of the Commutative Property in the equivalence of the expressions \(12a + 10 + a\) and \(10 + a + 12a\), here is a step-by-step outline with the missing step filled in:

Step 1: \(10 + 12a + a = 10 + a + 12a\) (Rearranging using the Commutative Property)
Step 2: \(10 + 13a = 10 + 13a\)
Step 3: The expressions are equivalent because they both equal the same value.

In Step 1, we apply the Commutative Property to rearrange the terms of \(12a + 10 + a\) so that they match the order of terms in \(10 + a + 12a\). This establishes the equivalency more clearly.

Answer 3

Substituting \(1\) for \(x\) in the equation \(5x + 3 = x \cdot 5 + 3\) is a test case for **the commutative property of multiplication**.

This property states that changing the order of the factors does not change the product. In this case, both expressions yield the same result when \(x = 1\), demonstrating that \(5x\) can be expressed as \(x \cdot 5\).

So the correct answer is:

**the commutative property of multiplication**.