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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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

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.

anonymous anonymous answered
2 months ago

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

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 months ago

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**.