Question
Which step contains an error using the Commutative Property of Addition in verifying
8+2+172-23+4=10+422+102-422+2+72？
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)
• Step 1
• Step 3
• No mistake was made.
• Step 2
8+2+172-23+4=10+422+102-422+2+72？
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)
• Step 1
• Step 3
• No mistake was made.
• Step 2
Answers
Answered by
GPT-4o mini
To identify the error in using the Commutative Property of Addition, we need to closely examine the steps given.
**Step 1:**
8 + 4 + x² - x² + 17x = 10 + 2 + 10x - 4x² + 7x + 4x²
- On the left-hand side, we have 8 + 4 + 17x, and it appears you are trying to manipulate terms on the right. However, 10x - 4x² + 7x + 4x² does not simplify correctly. Specifically, the terms involving \(x^2\) are not correctly accounted.
**Step 2:**
8 + 4 + 17x + x² - x² = 10 + 2 + 4x² - 4x² + 10x + 7x.
- Here, \(x² - x²\) cancels out correctly. However, looking closely, \(10 + 2\) gives us \(12\), and the right-hand side does not add up correctly once you combine similar terms.
**Step 3:**
12 + 17x + x² = 12 - x² + 17x.
- In this step, the \(x²\) term on the left-hand side is not correctly balanced with the right-hand side. You cannot just manipulate \(x²\) like that between equalities without ensuring all terms are correctly accounted for.
To summarize:
- The error lies in the first two steps, but the most significant one that causes the equation to become unbalanced is notably in **Step 1** due to incorrect grouping and simplification.
Thus, the answer is:
**Step 1**.
**Step 1:**
8 + 4 + x² - x² + 17x = 10 + 2 + 10x - 4x² + 7x + 4x²
- On the left-hand side, we have 8 + 4 + 17x, and it appears you are trying to manipulate terms on the right. However, 10x - 4x² + 7x + 4x² does not simplify correctly. Specifically, the terms involving \(x^2\) are not correctly accounted.
**Step 2:**
8 + 4 + 17x + x² - x² = 10 + 2 + 4x² - 4x² + 10x + 7x.
- Here, \(x² - x²\) cancels out correctly. However, looking closely, \(10 + 2\) gives us \(12\), and the right-hand side does not add up correctly once you combine similar terms.
**Step 3:**
12 + 17x + x² = 12 - x² + 17x.
- In this step, the \(x²\) term on the left-hand side is not correctly balanced with the right-hand side. You cannot just manipulate \(x²\) like that between equalities without ensuring all terms are correctly accounted for.
To summarize:
- The error lies in the first two steps, but the most significant one that causes the equation to become unbalanced is notably in **Step 1** due to incorrect grouping and simplification.
Thus, the answer is:
**Step 1**.