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
No mistake was made.
No mistake was made.
Step 2
Step 2
Step 1
Step 1
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
No mistake was made.
No mistake was made.
Step 2
Step 2
Step 1
Step 1
Step 3
Answers
Answered by
GPT-4o mini
To determine which step contains an error using the Commutative Property of Addition, let's analyze each step carefully:
**Step 1:**
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2 \)
Here, it appears that the left side correctly adds the constants and the terms, while the right side also adds properly. There doesn't seem to be any mistake in this step.
**Step 2:**
\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
In this step, let's simplify both sides:
Left side:
- Combine constants: \( 8 + 4 = 12 \)
- The \( x^2 \) terms cancel out: \( x^2 - x^2 = 0 \)
- The left side simplifies to: \( 12 + 17x \)
Right side:
- Combine \( 4x^2 - 4x^2 = 0 \), the constants: \( 10 + 2 = 12 \)
- Combine \( 10x + 7x = 17x \)
- The right side simplifies to: \( 12 + 17x \)
Thus, both sides are equal and match. There is no mistake in Step 2.
**Step 3:**
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Here, we have \( 12 + 17x + x^2 \) on the left and \( 12 - x^2 + 17x \) on the right.
On the left, you have \( x^2 \) as a positive term. On the right, you have \( -x^2 \) as a negative term. The left side does not equal the right side because of the difference in the signs of \( x^2 \).
Thus, Step 3 contains the error. Therefore, the correct answer is:
**Step 3.**
**Step 1:**
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2 \)
Here, it appears that the left side correctly adds the constants and the terms, while the right side also adds properly. There doesn't seem to be any mistake in this step.
**Step 2:**
\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
In this step, let's simplify both sides:
Left side:
- Combine constants: \( 8 + 4 = 12 \)
- The \( x^2 \) terms cancel out: \( x^2 - x^2 = 0 \)
- The left side simplifies to: \( 12 + 17x \)
Right side:
- Combine \( 4x^2 - 4x^2 = 0 \), the constants: \( 10 + 2 = 12 \)
- Combine \( 10x + 7x = 17x \)
- The right side simplifies to: \( 12 + 17x \)
Thus, both sides are equal and match. There is no mistake in Step 2.
**Step 3:**
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Here, we have \( 12 + 17x + x^2 \) on the left and \( 12 - x^2 + 17x \) on the right.
On the left, you have \( x^2 \) as a positive term. On the right, you have \( -x^2 \) as a negative term. The left side does not equal the right side because of the difference in the signs of \( x^2 \).
Thus, Step 3 contains the error. Therefore, the correct answer is:
**Step 3.**