// Numbas version: exam_results_page_options
{"name": "Expand brackets and solve an equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variable_groups": [], "variables": {"s1": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s1"}, "td": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..20)", "description": "", "name": "td"}, "b": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s2*random(1..12)", "description": "", "name": "b"}, "c": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(a*g=tc*f,tc+1,tc)", "description": "", "name": "c"}, "f": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..5)", "description": "", "name": "f"}, "s3": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s3"}, "d": {"templateType": "anything", "group": "Ungrouped variables", "definition": "if(b=td,td+1,td)", "description": "", "name": "d"}, "g": {"templateType": "anything", "group": "Ungrouped variables", "definition": "switch(f=1,random(2..5),f=2, random(3..5),f=3, random(2,4,5),f=4,random(3,5),random(2,3,4))", "description": "", "name": "g"}, "tc": {"templateType": "anything", "group": "Ungrouped variables", "definition": "s3*random(2..20)", "description": "", "name": "tc"}, "a": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12)", "description": "", "name": "a"}, "s2": {"templateType": "anything", "group": "Ungrouped variables", "definition": "random(1,-1)", "description": "", "name": "s2"}}, "ungrouped_variables": ["a", "c", "b", "d", "g", "f", "s3", "s2", "s1", "td", "tc"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "name": "", "pickQuestions": 0}], "name": "Expand brackets and solve an equation", "functions": {}, "showQuestionGroupNames": false, "parts": [{"stepsPenalty": 0, "scripts": {}, "gaps": [{"answer": "{f*d-b*g}/{g*a-f*c}", "vsetrange": [0, 1], "checkingaccuracy": 0.001, "showCorrectAnswer": true, "expectedvariablenames": [], "notallowed": {"message": "<p>Input your answer as a fraction or an integer. Do&nbsp;<span class=\"caps\">not</span>&nbsp;input the answer as a decimal.&nbsp;</p>", "showStrings": false, "partialCredit": 0, "strings": ["."]}, "showpreview": true, "checkingtype": "absdiff", "scripts": {}, "checkvariablenames": false, "type": "jme", "answersimplification": "all", "marks": 3, "vsetrangepoints": 5}], "type": "gapfill", "prompt": "\n\t\t\t<p>\\[\\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}\\]<br/><br/></p>\n\t\t\t      <p>$x =$ [[0]]</p>\n\t\t\t      <p>Click on \"Show steps\" to see a video of a solution of a similar problem.</p>\n\t\t\t", "steps": [{"type": "information", "prompt": "\n\t\t\t\t\t          <p>A video example worked through. The method in the video is slightly different from the method in the solution.</p>\n\t\t\t\t\t          <p>&nbsp;</p>\n\t\t\t\t\t          <p><iframe src=\"https://player.vimeo.com/video/8173488\" frameborder=\"0\" width=\"640\" height=\"480\"></iframe></p>\n\t\t\t\t\t          \n\t\t\t\t\t            \n\t\t\t\t\t            \n\t\t\t\t\t            \n\t\t\t\t\t", "showCorrectAnswer": true, "scripts": {}, "marks": 0}], "showCorrectAnswer": true, "marks": 0}], "statement": "\n\t<p>Solve the following linear equation for $x$.</p>\n\t  <p>Input your answer as a fraction or an integer. Do&nbsp;<span class=\"caps\">NOT</span>&nbsp;input the answer as a decimal.</p>\n\t  <p>&nbsp;</p>\n\t", "tags": ["ACC1012", "checked2015", "equations", "linear equation", "solving a linear equation in one variable", "solving equations", "Solving equations", "solving linear equations", "video"], "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "preamble": {"css": "", "js": ""}, "type": "question", "metadata": {"notes": "\n\t\t        \t\t        \t\t        \t\t    \t\t                                        \t\t    \t\t<p><strong>5/08/2012:</strong></p>\n\t\t        \t\t        \t\t        \t\t    \t\t                                        \t\t    \t\t    <p>Added more tags.</p>\n\t\t        \t\t        \t\t        \t\t    \t\t                                        \t\t    \t\t    <p>Added description.</p>\n\t\t        \t\t        \t\t        \t\t    \t\t                                        \t\t    \t\t    <p>Checked calculation. OK.</p>\n\t\t        \t\t        \t\t        \t\t    \t\t                                        \t\t    \n\t\t        \t\t        \t\t        \t\t    \t\t                                        \n\t\t        \t\t        \t\t        \t\t    \n\t\t        \t\t        \t\t        \n\t\t        \t\t        \n\t\t        \n\t\t", "licence": "Creative Commons Attribution 4.0 International", "description": "<p>Solve $\\displaystyle ax + b =\\frac{f}{g}( cx + d)$ for $x$.</p>\n<p>A video is included in Show steps which goes through a similar example.</p>"}, "variablesTest": {"condition": "", "maxRuns": 100}, "advice": "<p>Given the equation \\[\\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}\\] we first multiply both sides by $\\var{g}$ to get</p>\n<p>\\[\\simplify[std]{{g}*({a} * x + {b} )= {f}*({c} * x + {d})}.\\]</p>\n<p>Then expand both sides of this equation to get:</p>\n<p>\\[\\simplify[std]{{g*a} x + {g*b} = {f*c}x + {f*d}}.\\]</p>\n<p>and then&nbsp;collect together all the constant terms on the right hand-side, and collect together all the terms in $x$ on the left-hand side of the equation.</p>\n<p>The equation can then be written as:<br/>\\[\\simplify[std]{({g*a}-{f*c})x=({f*d}+{-g*b})}\\] i.e.<br/>\\[\\simplify{{g*a-f*c}x={f*d-b*g}}\\]<br/>which gives \\[x =\\simplify[std]{{(f*d-b*g)}/{(g*a-f*c)}}\\] as the solution.</p>\n<p><strong>Check the answer</strong></p>\n<p>You can check that this is the correct solution by inputting this solution back into the equation to see if it satisfies the equation.&nbsp;</p>\n<p>&nbsp;</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/"}]}