Question
Which step contains an error using the Commutative Property of Addition in verifying
?
Step 1:
Step 2:
Step 3:
(1 point)
8 + + 17x x2 − x2 + 4 = 10 + 4x2 + 10x − 4x2 + 2 + 7x
8 + 4 + x2 − x2 + 17x = 10 + 2 + 10x − 4x2 + 7x + 4x2
8 + 4 + 17x + x2 − x2 = 10 + 2 + 4x2 − 4x2 + 10x + 7x
12 + 17x + x2 = 12 − x2 + 17x
Step 1
Step 3
No mistake was made.
Step 2
?
Step 1:
Step 2:
Step 3:
(1 point)
8 + + 17x x2 − x2 + 4 = 10 + 4x2 + 10x − 4x2 + 2 + 7x
8 + 4 + x2 − x2 + 17x = 10 + 2 + 10x − 4x2 + 7x + 4x2
8 + 4 + 17x + x2 − x2 = 10 + 2 + 4x2 − 4x2 + 10x + 7x
12 + 17x + x2 = 12 − x2 + 17x
Step 1
Step 3
No mistake was made.
Step 2
Answers
Answered by
GPT-4o mini
To determine which step contains an error using the Commutative Property of Addition, let's analyze each step:
**Step 1:**
\( 8 + 17x + x^2 - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \)
**Step 2:**
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
**Step 3:**
\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
**Final step:**
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Now, let's break down what's happening in each step:
- **In Step 1**, all terms are correctly stated, but note the arrangement on the right side.
- **In Step 2**, there's a rearrangement, but it looks like both sides are attempting to simplify to follow a similar structure. All terms are present.
- **In Step 3**, no terms are omitted, and the arrangement maintains the same structure.
Now examining the simplification:
- The left side in Step 3 simplifies to: \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)).
- The right side in Step 3 simplifies incorrectly: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \) should give \( 12 + 17x \).
Thus, Step 2 contains an error in adding and organizing the terms correctly. It mixes them and doesn’t appropriately combine like terms.
The answer is **Step 2**.
**Step 1:**
\( 8 + 17x + x^2 - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \)
**Step 2:**
\( 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 7x + 4x^2 \)
**Step 3:**
\( 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \)
**Final step:**
\( 12 + 17x + x^2 = 12 - x^2 + 17x \)
Now, let's break down what's happening in each step:
- **In Step 1**, all terms are correctly stated, but note the arrangement on the right side.
- **In Step 2**, there's a rearrangement, but it looks like both sides are attempting to simplify to follow a similar structure. All terms are present.
- **In Step 3**, no terms are omitted, and the arrangement maintains the same structure.
Now examining the simplification:
- The left side in Step 3 simplifies to: \( 12 + 17x \) (since \( x^2 - x^2 = 0 \)).
- The right side in Step 3 simplifies incorrectly: \( 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \) should give \( 12 + 17x \).
Thus, Step 2 contains an error in adding and organizing the terms correctly. It mixes them and doesn’t appropriately combine like terms.
The answer is **Step 2**.