To determine which step contains an error using the Commutative Property of Addition, let's analyze each step systematically.
Step 1: \[ 8 + 4 + x^2 - x^2 + 17x = 10 + 2 + 10x - 4x^2 + 4x^2 \]
- On the left side: \( x^2 - x^2 \) cancels out.
- On the right side: \( -4x^2 + 4x^2 \) also cancels out. This step appears correct.
Step 2: \[ 8 + 4 + 17x + x^2 - x^2 = 10 + 2 + 4x^2 - 4x^2 + 10x + 7x \]
- The left side simplifies to \( 12 + 17x \).
- The right side simplifies to \( 12 + 10x + 7x \) which equals \( 12 + 17x \). This step also appears correct.
Step 3: \[ 12 + 17x + x^2 = 12 - x^2 + 17x \]
- The left side is \( 12 + 17x + x^2 \).
- The right side is \( 12 - x^2 + 17x \).
The issue here is that the term \( x^2 \) on the left side is incorrectly stated as \( -x^2 \) on the right side. The equation is not balanced due to this inconsistency.
Therefore, the error is found in:
Step 3.
1 answer