// Numbas version: exam_results_page_options
{"name": "Solving equations 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d", "s2", "s1", "t", "b1", "an2", "an1"], "name": "Solving equations 2", "tags": ["algebra", "algebraic fractions", "algebraic manipulation", "changing the subject of an equation", "rearranging equations", "solving", "Solving equations", "solving equations", "subject of an equation"], "advice": "<p>We can start by adding {-c} to both sides to get:<br/>\\[\\simplify{{t} / ({a} * x + {b})&nbsp; = {d -c}}\\]<br/>Taking the reciprocal of both sides of the equation gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\]</p>\n<p>Alternatively we could multiply both sides of the equation by $\\simplify{ {a}*x + {b}} $ to give \\[ \\simplify{ {t} = {d-c}({a}*x+{b})}\\]<br/>Both will give \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\].<br/>Hence \\[\\simplify{{a} * x = ({a * an1} / {an2})}\\]<br/>and so \\[\\simplify{x={an1}/{an2}}\\].</p>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers", "!noLeadingMinus"]}, "parts": [{"prompt": "<p>\\[\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\\]</p>\n<p>$x=\\;$ [[0]]</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"notallowed": {"message": "<p>Input as a fraction or an integer, not as a decimal.</p>", "showStrings": false, "strings": ["."], "partialCredit": 0}, "variableReplacements": [], "expectedvariablenames": [], "checkingaccuracy": 0.0001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "answersimplification": "std", "scripts": {}, "answer": "{an1}/{an2}", "marks": 2, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "showCorrectAnswer": true, "scripts": {}, "marks": 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": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "s2*random(1..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "if(a=abs(b1),abs(b1)+2,b1)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "abs(c)+random(2..9)", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "s2": {"definition": "random(1,-1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s2", "description": ""}, "s1": {"definition": "random(-1,1)", "templateType": "anything", "group": "Ungrouped variables", "name": "s1", "description": ""}, "b1": {"definition": "s1*random(1..10)", "templateType": "anything", "group": "Ungrouped variables", "name": "b1", "description": ""}, "t": {"definition": "random(2..8)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "an2": {"definition": "a*(d-c)", "templateType": "anything", "group": "Ungrouped variables", "name": "an2", "description": ""}, "an1": {"definition": "t-b*d+b*c", "templateType": "anything", "group": "Ungrouped variables", "name": "an1", "description": ""}}, "metadata": {"description": "<p>Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}