Question
Which step contains an error using the Commutative Property of Addition in verifying 8+x2+17x−x2+4=10+4x2+10x−4x2+2+7x ?
Step 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2
Step 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x
Step 3: 12+17x+x2=12−x2+17x
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
No mistake was made.
No mistake was made.
Step 3
Step 1: 8+4+x2−x2+17x=10+2+10x−4x2+7x +4x2
Step 2: 8+4+17x+x2−x2=10+2+4x2−4x2+10x+7x
Step 3: 12+17x+x2=12−x2+17x
(1 point)
Responses
Step 1
Step 1
Step 2
Step 2
No mistake was made.
No mistake was made.
Step 3
Answers
Answered by
GPT-4o mini
To determine if there is an error using the Commutative Property of Addition in the steps provided, let's break down each step carefully.
**Step 1**:
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
This simplifies to:
Left side: \( 8 + 4 + 17x = 12 + 17x \) (and the \( x^2 - x^2 \) cancels out)
Right side: \( 10 + 2 + 10x - 4x^2 + 4x^2 + 7x = 12 + 17x \) (the \( -4x^2 + 4x^2 \) cancels out as well)
No mistake is visible in this step: both sides equal \( 12 + 17x \).
**Step 2**:
This step reformulates both sides. It simplifies as follows:
Left side: \( 8 + 4 + 17x + x^2 - x^2 = 12 + 17x \)
Right side: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x = 12 + 17x \)
Again, no mistakes appear to be present.
**Step 3**:
In this step the simplification is shown as:
Left side: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Right side appears to be incorrect because \( 12 + 17x + x^2 \) on the left cannot equal \( 12 - x^2 + 17x \) on the right where it suggests that \( x^2 \) coined in but one side indicates a subtraction of \( x^2 \). This is inconsistent.
Thus, the error is contained in **Step 3**.
So, the correct answer is:
**Step 3**
**Step 1**:
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
This simplifies to:
Left side: \( 8 + 4 + 17x = 12 + 17x \) (and the \( x^2 - x^2 \) cancels out)
Right side: \( 10 + 2 + 10x - 4x^2 + 4x^2 + 7x = 12 + 17x \) (the \( -4x^2 + 4x^2 \) cancels out as well)
No mistake is visible in this step: both sides equal \( 12 + 17x \).
**Step 2**:
This step reformulates both sides. It simplifies as follows:
Left side: \( 8 + 4 + 17x + x^2 - x^2 = 12 + 17x \)
Right side: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x = 12 + 17x \)
Again, no mistakes appear to be present.
**Step 3**:
In this step the simplification is shown as:
Left side: \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Right side appears to be incorrect because \( 12 + 17x + x^2 \) on the left cannot equal \( 12 - x^2 + 17x \) on the right where it suggests that \( x^2 \) coined in but one side indicates a subtraction of \( x^2 \). This is inconsistent.
Thus, the error is contained in **Step 3**.
So, the correct answer is:
**Step 3**