// Numbas version: finer_feedback_settings
{"name": "Prerequisites: Solve a linear equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"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 as a decimal.</p>\n  \n  ", "tags": [], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Prerequisites: Solve a linear equation", "functions": {}, "variable_groups": [], "advice": "<p>If $\\simplify{{a}*x + {b}}=\\simplify{{c}*x + {d}}$, then we first subtract $\\var{c}x$ from each side.</p>\n  <p>We obtain $\\simplify{{a}x - {c}x+ {b}}= \\var{d}$.</p>\n  <p>Next we subtract $\\var{b}$ from each side (or add $\\var{-b}$ if you prefer - it means the same thing), to obtain $\\var{a}x - \\var{c}x = \\simplify{{d}-{b}}$.</p>\n  <p>In other words $\\simplify{{a}-{c}}x= \\simplify{{d}-{b}}$.</p>\n  <p>Now divide both sides by $\\simplify{{a-c}}$ to obtain $x=\\dfrac{\\simplify{{d-b}}}{\\simplify{{a-c}}}$ $=\\Large{\\simplify{{an1}/{an2}}}$.</p>", "ungrouped_variables": ["a", "c", "b", "d", "an1", "an2"], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"js": "", "css": ""}, "variables": {"d": {"name": "d", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-9..9)"}, "a": {"name": "a", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-9..9 except 0)"}, "an2": {"name": "an2", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "a-c"}, "an1": {"name": "an1", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "d-b"}, "b": {"name": "b", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(-9..9 except 0)"}, "c": {"name": "c", "group": "Ungrouped variables", "description": "", "templateType": "anything", "definition": "random(2..9 except a)"}}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle ax+b = cx+d$</p>"}, "parts": [{"adaptiveMarkingPenalty": 0, "prompt": "\n      <p>\\[\\simplify{{a} * x + {b}  = {c} * x + {d}}\\]</p>\n        <p>$x=\\;$ [[0]]</p>\n        \n      ", "showCorrectAnswer": true, "marks": 0, "customName": "", "gaps": [{"extendBaseMarkingAlgorithm": true, "vsetRangePoints": 5, "notallowed": {"strings": ["."], "message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "partialCredit": 0, "showStrings": false}, "marks": 1, "answerSimplification": "std", "checkingAccuracy": 0.0001, "customMarkingAlgorithm": "", "showFeedbackIcon": true, "type": "jme", "checkingType": "absdiff", "vsetRange": [0, 1], "adaptiveMarkingPenalty": 0, "showCorrectAnswer": true, "checkVariableNames": false, "valuegenerators": [], "unitTests": [], "useCustomName": false, "customName": "", "showPreview": true, "variableReplacementStrategy": "originalfirst", "failureRate": 1, "answer": "{an1}/{an2}", "variableReplacements": [], "scripts": {}}], "type": "gapfill", "sortAnswers": false, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "variableReplacements": [], "showFeedbackIcon": true, "unitTests": [], "extendBaseMarkingAlgorithm": true, "scripts": {}}], "type": "question", "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}]}], "contributors": [{"name": "Newcastle University Mathematics and Statistics", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/697/"}, {"name": "Timur Zaripov", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3272/"}]}