// Numbas version: exam_results_page_options
{"name": "Solving equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Solving equations", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "rearranging equations", "solving", "solving equations", "subject of an equation"], "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>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"stepspenalty": 1.0, "prompt": "\n        <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>\n        ", "gaps": [{"notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showstrings": false, "strings": ["."], "partialcredit": 0.0}, "checkingaccuracy": 0.0001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "std", "marks": 2.0, "answer": "{an1}/{an2}", "type": "jme"}], "steps": [{"prompt": "\n            <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>\n            ", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "\n    <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>\n    ", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(2..9)", "name": "a"}, "c": {"definition": "s2*random(1..9)", "name": "c"}, "b": {"definition": "if(a=abs(b1),abs(b1)+2,b1)", "name": "b"}, "d": {"definition": "abs(c)+random(2..9)", "name": "d"}, "s2": {"definition": "random(1,-1)", "name": "s2"}, "s1": {"definition": "random(-1,1)", "name": "s1"}, "t": {"definition": "random(2..8)", "name": "t"}, "an2": {"definition": "a*(d-c)", "name": "an2"}, "an1": {"definition": "t-b*d+b*c", "name": "an1"}, "b1": {"definition": "s1*random(1..10)", "name": "b1"}}, "metadata": {"notes": "\n        \t\t<p><strong>5/08/2012:</strong></p>\n        \t\t    <p>Added tags.</p>\n        \t\t    <p>Added description.</p>\n        \t\t    <p>Checked calculation.OK.</p>\n        \t\t    <p>Improved display in content areas.</p>\n        \t\t", "description": "<p>Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}]}], "contributors": [{"name": "Bill Foster", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/6/"}]}