// Numbas version: finer_feedback_settings {"name": "Ann'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": [{"parts": [{"stepsPenalty": 1, "prompt": "\n
\\[\\simplify{{s} / ({a} * x + {b}) = {t} / ({c} * x + {d})}\\]
\n$x=\\;$ [[0]]
\nIf you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.
\n \n \n ", "marks": 0, "scripts": {}, "steps": [{"type": "information", "prompt": "\nRearrange 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.
Input as a fraction or an integer, not as a decimal.
", "strings": ["."]}, "answersimplification": "std", "vsetrangepoints": 5, "marks": 2, "checkingtype": "absdiff", "checkingaccuracy": 0.0001, "answer": "{an1}/{an2}", "vsetrange": [0, 1], "showCorrectAnswer": true}], "showCorrectAnswer": true}], "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "subject of an equation"], "variable_groups": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "Solve for $x$: $\\displaystyle \\frac{s}{ax+b} = \\frac{t}{cx+d}$
", "notes": "\n \t\t \t\t\t\t\t\t \t\t \t\t\t\t \n \t\t"}, "statement": "\nSolve the following equation for $x$.
\nInput your answer as a fraction or an integer as appropriate and not as a decimal.
\n ", "preamble": {"css": "", "js": ""}, "functions": {}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickQuestions": 0, "questions": [], "pickingStrategy": "all-ordered"}], "type": "question", "advice": "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}}.\\]