\\frac{3x + 1}{2} = \frac{2x - 5}{3} \quad \text{(cross multiplication)}\
\3(3x + 1) = 2(2x - 5)\
\9x + 3 = 4x - 10 \quad (-4x)\
\5x + 3 = -10 \quad (-3)\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Linear Equations" ], "new_concepts": [ "Fractional Equations", "Cross Multiplication" ], "current_concepts": [ "Linear Equations", "Fractional Equations", "Cross Multiplication" ] } ## Apply cross-multiplication Using the *Linear Equations* knowledge point $$ \begin{aligned} \frac{3x + 1}{2} &= \frac{2x - 5}{3} \ 3(3x + 1) &= 2(2x - 5) \end{aligned} $$ ## Expand both sides Using the *Linear Equations* knowledge point $$ \begin{aligned} 9x + 3 &= 4x - 10 \end{aligned} $$ ## Subtract 4x from both sides Using the *Linear Equations* knowledge point $$ \begin{aligned} 5x + 3 &= -10 \end{aligned} $$ ## Subtract 3 from both sides Using the *Linear Equations* knowledge point $$ \begin{aligned} 5x &= -13 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} x &= -\frac{13}{5} \end{aligned} $$ $x = -\frac{13}{5}$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply cross-multiplication

Expand both sides

Subtract 4x from both sides

Subtract 3 from both sides

Solve for x

Answer: