// Numbas version: exam_results_page_options
{"name": "Luis's copy of Solving equations", "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": "<p><strong>5/08/2012:</strong></p>\n    <p>Added tags.</p>\n    <p>Added description.</p>\n    <p>Checked calculation.OK.</p>\n    <p>Improved display in content areas.</p>", "description": "<p>Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "advice": "<p>Rearrange the equation by adding {-c} to both sides to get:<br/>\\[\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]<br/>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)<br/>and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.<br/>Hence \\[\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\\]<br/>and so \\[\\simplify{x={an1}/{an2}}\\] is the solution on dividing both sides by {a}.</p>", "showQuestionGroupNames": false, "variable_groups": [], "preamble": {"css": "", "js": ""}, "type": "question", "parts": [{"scripts": {}, "stepsPenalty": 1, "showCorrectAnswer": true, "marks": 0, "gaps": [{"scripts": {}, "type": "jme", "showpreview": true, "answer": "{an1}/{an2}", "checkvariablenames": false, "vsetrangepoints": 5, "marks": 2, "vsetrange": [0, 1], "expectedvariablenames": [], "showCorrectAnswer": true, "checkingtype": "absdiff", "notallowed": {"strings": ["."], "partialCredit": 0, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false}, "answersimplification": "std", "checkingaccuracy": 0.0001}], "type": "gapfill", "prompt": "<p>\\[\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\\]</p>\n      <p>$x=\\;$ [[0]]</p>\n      <p>If you want help in solving the equation, click on Show steps. If you do so then you will lose 1 mark.</p>\n      <p>Input all numbers as fractions or integers and not as decimals.</p>", "steps": [{"scripts": {}, "marks": 0, "prompt": "<p>Rearrange the equation by adding {-c} to both sides to get:<br/>\\[\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]</p>\n          <p>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)</p>\n          <p>and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.</p>\n          <p>Solve this equation for $x$.</p>", "type": "information", "showCorrectAnswer": true}]}], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "question_groups": [{"questions": [], "pickingStrategy": "all-ordered", "pickQuestions": 0, "name": ""}], "statement": "<p>Solve the following equation for $x$.</p>\n  <p>Input your answer as a fraction or an integer as appropriate and not&nbsp;as a decimal.</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "MAS1601", "mas1601", "rearranging equations", "solving", "solving equations", "Solving equations", "subject of an equation"], "variables": {"an1": {"description": "", "group": "Ungrouped variables", "name": "an1", "definition": "t-b*d+b*c", "templateType": "anything"}, "b1": {"description": "", "group": "Ungrouped variables", "name": "b1", "definition": "s1*random(1..10)", "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"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "if(a=abs(b1),abs(b1)+2,b1)", "templateType": "anything"}, "an2": {"description": "", "group": "Ungrouped variables", "name": "an2", "definition": "a*(d-c)", "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"}, "t": {"description": "", "group": "Ungrouped variables", "name": "t", "definition": "random(2..8)", "templateType": "anything"}}, "name": "Luis's copy of Solving equations", "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/"}]}