// Numbas version: exam_results_page_options {"name": "Luis's copy of 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": [{"ungrouped_variables": ["a", "c", "b", "d", "s", "t", "an2", "an1"], "metadata": {"description": "

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

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\\[\\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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Resuelve la siguiente ecuación para $ x $.

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Ingrese su respuesta como una fracción o un entero, según corresponda y no como un decimal.

", "name": "Luis's copy of Solve an equation with reciprocals", "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Luis Hernandez", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2870/"}]}