Use the Commutative Property to determine the missing step in proving the equivalence of 12a+10+a=10+a+12a .

Question

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:
10+12a+a=10+13a
12a+10+a−10=10+a+12a−10
12a+10+a−a=10+a+12a−a
12a+10=10+12a

Answer 1

To find the missing step using the Commutative Property, we need to rearrange the terms in the expression \(12a + 10 + a\).

The Commutative Property states that the order in which you add numbers does not change the sum.

Starting from the original expression \(12a + 10 + a\), we can rearrange it as:

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

Then we can combine like terms to reach Step 2, which is \(10 + 13a = 10 + 13a\).

The answer is: 10 + 12a + a = 10 + 13a.

Answer 2

Substituting 1 for x in the equation 5x + 3=x⋅5 + 3 is a test case for which property? Responses:
The Associative Property of Addition
The Commutative Property of Addition
The Associative Property of Multiplication
The Commutative Property of Multiplication

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 the order in which two numbers are multiplied does not affect their product. In the given equation, \(5x\) and \(x \cdot 5\) demonstrate this property, as they are rearrangements of the same multiplication operation.

So, the correct response is: The Commutative Property of Multiplication.

Answer 4

Which step contains an error using the Commutative Property of Addition in verifying 8+x^2+17x−x^2+4=10+4x^2+10x−4x^2+2+7x
Step 1: 8+4+x^2−x^2+17x=10+2+10x−4x^2+7x +4x^2
Step 2: 8+4+17x+x^2−x^2=10+2+4x^2−4x^2+10x+7x
Step 3: 12+17x+x^2=12−x^2+17x
Responses:
Step 3
Step 1
Step 2
No mistake was made.

Answer 5

To find the error in the steps using the Commutative Property of Addition, let's analyze each step in detail.

Review of Steps:

1. Step 1: \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
   This step rearranges the terms on both sides. It looks correct as it follows the Commutative Property.

2. Step 2: \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
   This step (specifically the right side) seems to make an error in how the terms are combined. After simplifying, \(4x^2 - 4x^2\) should cancel out, but the way it is presented suggests that there are additional terms that complicate it unnecessarily.

3. Step 3: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
   After performing operations in the previous steps, this step should not contain the \( - x^2 \) term, because the \(x^2\) should cancel out, not remain on the right side.

Conclusion:

The primary issue originates in Step 2. The addition of terms on the right side is not done properly when mixing \(10x\) and \(7x\), as well as the treatment of \(4x^2\).

Thus, the error is in Step 2.

Final Answer: Step 2