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
Step 2
Step 2
No mistake was made.
No mistake was made.
Step 1
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
Step 2
Step 2
No mistake was made.
No mistake was made.
Step 1
Answers
Answered by
GPT-4o mini
To identify the error in the steps of verifying the equation using the Commutative Property of Addition, let's analyze each step and check the operations:
**Step 1:**
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
In this step, the Commutative Property is used correctly to rearrange terms. No mistakes are made up to this point.
**Step 2:**
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
Here, the terms are rearranged. One should simplify \( 4x^2 - 4x^2 \) to 0, which should correct the expression.
**Step 3:**
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
This step has a mistake. In the left-hand expression, the \( x^2 - x^2 \) terms should cancel out to 0, and thus we would only have \( 12 + 17x \) on the left-hand side, not including \( x^2 \).
The correct comparison after simplification would only involve evaluating \( 12 + 17x \) on the left and simplifying \( 12 + 17x \) on the right correctly without introducing \( -x^2 \).
Therefore, the error occurs in **Step 3.**
**Step 1:**
\[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \]
In this step, the Commutative Property is used correctly to rearrange terms. No mistakes are made up to this point.
**Step 2:**
\[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
Here, the terms are rearranged. One should simplify \( 4x^2 - 4x^2 \) to 0, which should correct the expression.
**Step 3:**
\[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
This step has a mistake. In the left-hand expression, the \( x^2 - x^2 \) terms should cancel out to 0, and thus we would only have \( 12 + 17x \) on the left-hand side, not including \( x^2 \).
The correct comparison after simplification would only involve evaluating \( 12 + 17x \) on the left and simplifying \( 12 + 17x \) on the right correctly without introducing \( -x^2 \).
Therefore, the error occurs in **Step 3.**