current objective
solve proportions

question
solve: $\frac{a}{a - 1} = -\frac{4}{3}$.

provide your answer below:

$a = \square$

Question

current objective
solve proportions

question
solve: $\frac{a}{a - 1} = -\frac{4}{3}$.

provide your answer below:

$a = \square$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Rational Equations", "Proportional Reasoning" ], "new_concepts": [], "current_concepts": [ "Solving Rational Equations", "Proportional Reasoning" ] } ## Cross-multiply to eliminate fractions $$ \begin{aligned} \frac{a}{a - 1} &= -\frac{4}{3} \ 3a &= -4(a - 1) \end{aligned} $$ ## Distribute and solve for a $$ \begin{aligned} 3a &= -4a + 4 \ 7a &= 4 \ a &= \frac{4}{7} \end{aligned} $$ ## Verify the solution $$ \begin{aligned} a - 1 &= \frac{4}{7} - 1 = -\frac{3}{7} eq 0 \ \frac{\frac{4}{7}}{-\frac{3}{7}} &= -\frac{4}{3} \end{aligned} $$ Solve: $\frac{a}{a - 1} = -\frac{4}{3}$. Provide your answer below: $a =$ $\frac{4}{7}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Cross-multiply to eliminate fractions

Distribute and solve for a

Verify the solution

Answer: