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 3
Step 3
No mistake was made.
No mistake was made.
Step 1
Step 1
Step 2
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 3
Step 3
No mistake was made.
No mistake was made.
Step 1
Step 1
Step 2
Answers
Answered by
GPT-4o mini
To analyze the steps provided for any mistakes using the Commutative Property of Addition, we can break down what each step claims to do and check for correctness.
1. **Step 1:** \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
Here, the left side simplifies to \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)). The right side simplifies to \( 12 + 10x + 7x = 12 + 17x \) (because \( -4x^2 + 4x^2 = 0 \)). So, this step appears to be correct.
2. **Step 2:** \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
The left-hand side simplifies as before to \( 12 + 17x \). The right-hand side simplifies to \( 12 + 10x + 7x \) which simplifies to \( 12 + 17x \). Thus, this step is also correct.
3. **Step 3:** \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Here, the left side is \( 12 + 17x + x^2 \), and the right side is \( 12 - x^2 + 17x \).
The mistake here is that the left side has a \( +x^2 \), while the right side has a \( -x^2 \). This means that this step contains an error.
Thus, the answer is:
**Step 3**
1. **Step 1:** \( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
Here, the left side simplifies to \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)). The right side simplifies to \( 12 + 10x + 7x = 12 + 17x \) (because \( -4x^2 + 4x^2 = 0 \)). So, this step appears to be correct.
2. **Step 2:** \( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
The left-hand side simplifies as before to \( 12 + 17x \). The right-hand side simplifies to \( 12 + 10x + 7x \) which simplifies to \( 12 + 17x \). Thus, this step is also correct.
3. **Step 3:** \( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Here, the left side is \( 12 + 17x + x^2 \), and the right side is \( 12 - x^2 + 17x \).
The mistake here is that the left side has a \( +x^2 \), while the right side has a \( -x^2 \). This means that this step contains an error.
Thus, the answer is:
**Step 3**