question

solve $c = \frac{2}{a} + \frac{b}{5}$ for $a$.

provide your answer below:

$a = \square$

Question

question

solve $c = \frac{2}{a} + \frac{b}{5}$ for $a$.

provide your answer below:

$a = \square$

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": [ "Solving Rational Equations", "Solving Linear Equations" ], "new_concepts": [ "Literal Equations" ], "current_concepts": [ "Solving Rational Equations", "Solving Linear Equations", "Literal Equations" ] } ## Isolate the term containing the variable a Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} c &= \frac{2}{a} + \frac{b}{5} \ c - \frac{b}{5} &= \frac{2}{a} \end{aligned} $$ ## Combine the terms on the left side Using the *Solving Rational Equations* knowledge point $$ \begin{aligned} \frac{5c}{5} - \frac{b}{5} &= \frac{2}{a} \ \frac{5c - b}{5} &= \frac{2}{a} \end{aligned} $$ ## Take the reciprocal of both sides Using the *Solving Rational Equations* knowledge point $$ \begin{aligned} \frac{5}{5c - b} &= \frac{a}{2} \end{aligned} $$ ## Solve for a by multiplying both sides by 2 Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} a &= \frac{10}{5c - b} \end{aligned} $$ Solve $c = \frac{2}{a} + \frac{b}{5}$ for $a$. $a =$ $\frac{10}{5c - b}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Rational Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Isolate the term containing the variable a

Combine the terms on the left side

Take the reciprocal of both sides

Solve for a by multiplying both sides by 2

Answer: