Let's analyze the student's solution step by step:
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Line 1: \( x + 2(x + 1) = 17 \) becomes \( x + 2x + 2 = 17 \) (not 1).
- Here is the mistake. The student incorrectly expanded \( 2(x + 1) \). The correct expansion should be \( 2x + 2 \).
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Line 2: \( 3x + 1 = 17 \) is derived from Line 1, and it should actually be \( 3x + 2 = 17 \).
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Line 3: The simplification to \( 3x = 16 \) is incorrect due to the previous mistake. The correct equation should have been \( 3x + 2 = 17\), leading to \( 3x = 15 \).
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Line 4: Claims \( x = \frac{16}{3} \) is therefore incorrect based on the previous mistakes.
To answer your questions:
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Identify the Property used to go from Line 2 to Line 3: This should actually involve the Subtraction Property of Equality, but in this case, since Line 2 itself is incorrect, this property was not applied correctly.
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Which line has a mistake? Line 1 has a mistake in the expansion.
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What should have been the correct answer for the equation?
- Following the correct derivation: From \( 3x + 2 = 17 \):
- Subtract 2 from both sides:
- \( 3x = 15 \)
- Divide by 3:
- \( x = 5 \)
- Therefore, the correct answer is x = 5.
- Following the correct derivation: From \( 3x + 2 = 17 \):