yusuf tried to solve an equation step by step.

\\frac{1}{4}r + 2 = 10\

\\frac{1}{4}r = 12\quad \text{step 1}\

\
= 48\quad \text{step 2}\

Question

yusuf tried to solve an equation step by step.

\\frac{1}{4}r + 2 = 10\

\\frac{1}{4}r = 12\quad \text{step 1}\

\
 = 48\quad \text{step 2}\

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Two-Step Equations", "Error Analysis in Equations" ], "new_concepts": [], "current_concepts": [ "Two-Step Equations", "Error Analysis in Equations" ] } ## Analyze the original equation and Step 1 $$ \begin{aligned} &\text{Original equation: } \frac{1}{4}r + 2 = 10\ &\text{Correct first step: } \frac{1}{4}r = 10 - 2 \implies \frac{1}{4}r = 8\ &\text{Yusuf's Step 1: } \frac{1}{4}r = 12 \end{aligned} $$ ## Identify the error in Step 1 $$ \begin{aligned} &\text{Yusuf added 2 to 10 instead of subtracting 2.}\ &\text{Error occurred in Step 1.} \end{aligned} $$ ## Determine the correct solution $$ \begin{aligned} &\frac{1}{4}r = 8\ &r = 8 \times 4\ &r = 32 \end{aligned} $$ Yusuf made a mistake in Step 1. He added 2 to the right side of the equation instead of subtracting 2. The correct steps are: $$ \begin{aligned} \frac{1}{4}r + 2 &= 10 \ \frac{1}{4}r &= 8 \quad \text{(Step 1)} \ r &= 32 \quad \text{(Step 2)} \end{aligned} $$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Error Analysis in Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Analyze the original equation and Step 1

Identify the error in Step 1

Determine the correct solution

Answer: