6. error analysis: a student solved the equation $2(x - 4) = 16$ and got $x = 10$. are they correct? show your work to justify your answer.

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Multi-Step Equations", "Algebraic Error Analysis" ], "new_concepts": [], "current_concepts": [ "Solving Multi-Step Equations", "Algebraic Error Analysis" ] } ## Solve the given equation $$ \begin{aligned} 2(x - 4) &= 16 \ x - 4 &= 8 \ x &= 12 \end{aligned} $$ ## Check the student's solution $$ \begin{aligned} x_{\text{student}} &= 10 \ 2(10 - 4) &= 2(6) = 12 eq 16 \end{aligned} $$ ## Identify the error $$ \begin{aligned} 2(10) - 4 &= 16 \ 20 - 4 &= 16 \end{aligned} $$ No, the student is not correct. The correct solution is $x = 12$. The student likely forgot to distribute the $2$ to the $-4$, solving $2x - 4 = 16$ instead of $2x - 8 = 16$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Multi-Step Equations" ] }

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Solve the given equation

Check the student's solution

Identify the error

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