// Numbas version: finer_feedback_settings
{"name": "Solve a linear equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"d": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9)", "name": "d", "description": ""}, "an1": {"group": "Ungrouped variables", "templateType": "anything", "definition": "d-b", "name": "an1", "description": ""}, "c": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(2..9 except a)", "name": "c", "description": ""}, "an2": {"group": "Ungrouped variables", "templateType": "anything", "definition": "a-c", "name": "an2", "description": ""}, "b": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9 except 0)", "name": "b", "description": ""}, "a": {"group": "Ungrouped variables", "templateType": "anything", "definition": "random(-9..9 except 0)", "name": "a", "description": ""}}, "ungrouped_variables": ["a", "c", "b", "d", "an1", "an2"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "name": "Solve a linear equation", "functions": {}, "showQuestionGroupNames": false, "parts": [{"scripts": {}, "gaps": [{"answer": "{an1}/{an2}", "showCorrectAnswer": true, "vsetrange": [0, 1], "checkingaccuracy": 0.0001, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"showStrings": false, "message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "strings": ["."], "partialCredit": 0}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "type": "jme", "answersimplification": "std", "marks": 1, "vsetrangepoints": 5}], "type": "gapfill", "showCorrectAnswer": true, "prompt": "\n      <p>\\[\\simplify{{a} * x + {b}  = {c} * x + {d}}\\]</p>\n        <p>$x=\\;$ [[0]]</p>\n        \n      ", "marks": 0}], "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": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "checked2015", "rearranging equations", "SFY0001", "solving", "solving equations", "Solving equations", "subject of an equation"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n            \t\t        \t\t\t\t\t\t        \t\t    \t\t\t\t        \n            \t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve for $x$: $\\displaystyle ax+b = cx+d$</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "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>", "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/"}]}