solve for x using cross multiplication.

\\frac{3x - 3}{4} = \frac{2x + 1}{3}\

$x = ?$

Question

solve for x using cross multiplication.

\\frac{3x - 3}{4} = \frac{2x + 1}{3}\

$x = ?$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Distributive Property", "Algebraic Simplification", "Linear Equations" ], "new_concepts": [ "Cross Multiplication", "Rational Equations" ], "current_concepts": [ "Cross Multiplication", "Distributive Property", "Algebraic Simplification", "Linear Equations" ] } ## Set up the cross multiplication To solve the rational equation, we multiply the numerator of each side by the denominator of the other side. $$ 3(3x - 3) = 4(2x + 1) $$ ## Apply the distributive property Using the **Distributive Property** knowledge point $$ \begin{aligned} 3 \cdot 3x - 3 \cdot 3 &= 4 \cdot 2x + 4 \cdot 1 \ 9x - 9 &= 8x + 4 \end{aligned} $$ ## Isolate the variable term Using the **Linear Equations** knowledge point $$ \begin{aligned} 9x - 8x - 9 &= 4 \ x - 9 &= 4 \end{aligned} $$ ## Solve for x Using the **Algebraic Simplification** knowledge point $$ \begin{aligned} x &= 4 + 9 \ x &= 13 \end{aligned} $$ Solve for x using cross multiplication. $$\frac{3x - 3}{4} = \frac{2x + 1}{3}$$ $x =$ 13 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Linear Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Set up the cross multiplication

Apply the distributive property

Isolate the variable term

Solve for x

Answer: