// Numbas version: exam_results_page_options {"name": "Luis's copy of Solve an equation with a reciprocal", "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", "s2", "s1", "b1", "t", "an2", "an1"], "metadata": {"notes": "\n\t\t \t\t \t\t \t\t \t\t
5/08/2012:
\n\t\t \t\t \t\t \t\t \t\tAdded tags.
\n\t\t \t\t \t\t \t\t \t\tAdded description.
\n\t\t \t\t \t\t \t\t \t\tChecked calculation.OK.
\n\t\t \t\t \t\t \t\t \t\tImproved display in content areas.
\n\t\t \t\t \t\t \t\t \n\t\t \t\t \t\t \n\t\t \t\t \n\t\t \n\t\t", "description": "Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$
", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "Rearrange the equation by adding {-c} to both sides to get:
\\[\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]
This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)
and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.
Hence \\[\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\\]
and so \\[\\simplify{x={an1}/{an2}}\\] is the solution on dividing both sides by {a}.
Input as a fraction or an integer, not as a decimal.
", "showStrings": false}, "type": "jme", "vsetrange": [0, 1], "checkvariablenames": false, "showCorrectAnswer": true, "checkingtype": "absdiff", "vsetrangepoints": 5, "answersimplification": "std", "answer": "{an1}/{an2}"}], "type": "gapfill", "prompt": "\n\t\t\t\\[\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\\]
\n\t\t\t$x=\\;$ [[0]]
\n\t\t\tIf you want help in solving the equation, click on \"Show steps\". If you do so then you will lose 1 mark.
\n\t\t\tInput all numbers as fractions or integers and not as decimals.
\n\t\t\t \n\t\t\t", "steps": [{"scripts": {}, "marks": 0, "prompt": "\n\t\t\t\t\tRearrange the equation by adding {-c} to both sides to get:
\\[\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]
This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)
\n\t\t\t\t\tand so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.
\n\t\t\t\t\tSolve this equation for $x$.
\n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t \n\t\t\t\t\t", "type": "information", "showCorrectAnswer": true}]}], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "statement": "\n\tSolve the following equation for $x$.
\n\tInput your answer as a fraction or an integer as appropriate and not as a decimal.
\n\t \n\t \n\t \n\t \n\t", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "tags": ["ACC1012", "algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "solving", "solving equations", "Solving equations", "subject of an equation"], "variables": {"b1": {"description": "", "group": "Ungrouped variables", "name": "b1", "definition": "s1*random(1..10)", "templateType": "anything"}, "an1": {"description": "", "group": "Ungrouped variables", "name": "an1", "definition": "t-b*d+b*c", "templateType": "anything"}, "d": {"description": "", "group": "Ungrouped variables", "name": "d", "definition": "abs(c)+random(2..9)", "templateType": "anything"}, "s2": {"description": "", "group": "Ungrouped variables", "name": "s2", "definition": "random(1,-1)", "templateType": "anything"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(2..9)", "templateType": "anything"}, "t": {"description": "", "group": "Ungrouped variables", "name": "t", "definition": "random(2..8)", "templateType": "anything"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "if(a=abs(b1),abs(b1)+2,b1)", "templateType": "anything"}, "c": {"description": "", "group": "Ungrouped variables", "name": "c", "definition": "s2*random(1..9)", "templateType": "anything"}, "s1": {"description": "", "group": "Ungrouped variables", "name": "s1", "definition": "random(-1,1)", "templateType": "anything"}, "an2": {"description": "", "group": "Ungrouped variables", "name": "an2", "definition": "a*(d-c)", "templateType": "anything"}}, "name": "Luis's copy of Solve an equation with a reciprocal", "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/"}]}