// Numbas version: finer_feedback_settings
{"name": "Solving equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-1,1)", "name": "s1", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "if(a=abs(b1),abs(b1)+2,b1)", "name": "b", "description": ""}, "d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "abs(c)+random(2..9)", "name": "d", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s2*random(1..9)", "name": "c", "description": ""}, "an2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "a*(d-c)", "name": "an2", "description": ""}, "b1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "s1*random(1..10)", "name": "b1", "description": ""}, "an1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "t-b*d+b*c", "name": "an1", "description": ""}, "s2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(1,-1)", "name": "s2", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9)", "name": "a", "description": ""}, "t": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..8)", "name": "t", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d", "s2", "s1", "b1", "t", "an2", "an1"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Solving equations", "showQuestionGroupNames": false, "functions": {}, "parts": [{"marks": 0, "scripts": {}, "gaps": [{"answer": "{an1}/{an2}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "std", "marks": 2, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "steps": [{"type": "information", "showCorrectAnswer": true, "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>", "scripts": {}, "marks": 0}], "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>", "stepsPenalty": 1}], "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "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"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "preamble": {"css": "", "js": ""}, "type": "question", "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>", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$</p>"}, "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>", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}]}