Question
Which step contains an error, using the community property of addition and verifying 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x?
Answers
Answered by
GPT-4o mini
To verify where the error occurs in the equation \( 8 + x^2 + 17x - x^2 + 4 = 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \), let's simplify both sides step by step.
**Left Side:**
1. Start with \( 8 + x^2 + 17x - x^2 + 4 \).
2. Combine like terms:
- The \( x^2 \) terms: \( x^2 - x^2 = 0 \)
- The constants: \( 8 + 4 = 12 \)
- The linear terms: \( 17x \)
3. So, the left side simplifies to \( 12 + 17x \).
**Right Side:**
1. Start with \( 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \).
2. Combine like terms:
- The \( x^2 \) terms: \( 4x^2 - 4x^2 = 0 \)
- The constants: \( 10 + 2 = 12 \)
- The linear terms: \( 10x + 7x = 17x \)
3. So, the right side simplifies to \( 12 + 17x \).
Now compare simplified forms of both sides:
- Left side: \( 12 + 17x \)
- Right side: \( 12 + 17x \)
Since both sides are equal after simplification, no error appears in the steps leading to the simplification of this equation.
However, if there were to be an error, it could mistakenly stem from incorrect distribution or combining of terms. In this specific case, it seems that both sides have been correctly simplified to the same expression: \( 12 + 17x \). Thus, if you were unable to find an error, it may indicate that the original statement of miscalculating the equation does not exist as per the calculations shown.
If any specific step needs re-evaluation for inaccuracies, please clarify.
**Left Side:**
1. Start with \( 8 + x^2 + 17x - x^2 + 4 \).
2. Combine like terms:
- The \( x^2 \) terms: \( x^2 - x^2 = 0 \)
- The constants: \( 8 + 4 = 12 \)
- The linear terms: \( 17x \)
3. So, the left side simplifies to \( 12 + 17x \).
**Right Side:**
1. Start with \( 10 + 4x^2 + 10x - 4x^2 + 2 + 7x \).
2. Combine like terms:
- The \( x^2 \) terms: \( 4x^2 - 4x^2 = 0 \)
- The constants: \( 10 + 2 = 12 \)
- The linear terms: \( 10x + 7x = 17x \)
3. So, the right side simplifies to \( 12 + 17x \).
Now compare simplified forms of both sides:
- Left side: \( 12 + 17x \)
- Right side: \( 12 + 17x \)
Since both sides are equal after simplification, no error appears in the steps leading to the simplification of this equation.
However, if there were to be an error, it could mistakenly stem from incorrect distribution or combining of terms. In this specific case, it seems that both sides have been correctly simplified to the same expression: \( 12 + 17x \). Thus, if you were unable to find an error, it may indicate that the original statement of miscalculating the equation does not exist as per the calculations shown.
If any specific step needs re-evaluation for inaccuracies, please clarify.