// Numbas version: exam_results_page_options {"name": "Solve an equation with reciprocals", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"tags": [], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "statement": "\n

Solve the following equation for $x$.

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Input your answer as a fraction or an integer as appropriate and not as a decimal.

\n ", "name": "Solve an equation with reciprocals", "parts": [{"useCustomName": false, "prompt": "\n

\\[\\simplify{{s} / ({a} * x + {b}) = {t} / ({c} * x + {d})}\\]

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$x=\\;$ [[0]]

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If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.

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Rearrange the equation by cross-multiplying to get:
\\[\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\\]
Multiply out to get \\[\\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.\\] Now solve this linear equation.

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Input as a fraction or an integer, not as a decimal.

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Solve for $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$

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Rearrange the equation by cross-multiplying to get:
\\[\\simplify{{s}*({c} * x + {d}) = {t} *({a} * x + {b})}\\]
Multiply out to get \\[\\simplify{{s*c}*x+{s*d}={t*a}*x+{t*b}}.\\] Now this is a linear equation which is solved in the following steps: \\[\\simplify{{s*c-t*a}*x={t*b-s*d}}\\] and then \\[\\simplify{x={t*b-s*d}/{s*c-t*a}}.\\]

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