leon tried to solve an equation step by step.

\\frac{1}{2}w - 12 = 18\

\\frac{1}{2}w = 30\ step 1

\w = 15\ step 2

Question

leon tried to solve an equation step by step.

\\frac{1}{2}w - 12 = 18\

\\frac{1}{2}w = 30\ step 1

\w = 15\ step 2

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Linear Equations", "Two-Step Equations", "Fractional Coefficients" ], "new_concepts": [ "Error Analysis in Equations" ], "current_concepts": [ "Linear Equations", "Two-Step Equations", "Fractional Coefficients", "Error Analysis in Equations" ] } ## Analyze Step 1 $$ \begin{aligned} &\frac{1}{2}w - 12 = 18 \ &\frac{1}{2}w = 18 + 12 \ &\frac{1}{2}w = 30 \end{aligned} $$ ## Analyze Step 2 $$ \begin{aligned} &\frac{1}{2}w = 30 \ &w = 30 \times 2 \ &w = 60 eq 15 \end{aligned} $$ Leon made a mistake in Step 2. Instead of multiplying both sides by 2 to solve for $w$, he divided by 2. The correct solution is $w = 60$. { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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