// Numbas version: exam_results_page_options
{"name": "Solving equations. (Video)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Solving equations. (Video)", "tags": ["Solving equations", "equations", "linear equation", "solving a linear equation in one variable", "solving equations", "solving linear equations", "video"], "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>", "rulesets": {"std": ["all", "!collectNumbers", "fractionNumbers"]}, "parts": [{"stepspenalty": 0.0, "prompt": "<p>\\[\\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}\\]<br/>Input your answer as a fraction or an integer. Do <span class=\"caps\">NOT</span> input the answer as a decimal.</p>\n        <p>$x =$ [[0]]</p>\n        <p>Click on Show steps to see a video of a solution of a similar problem.</p>", "gaps": [{"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, "strings": ["."], "partialcredit": 0.0}, "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0.0, 1.0], "vsetrangepoints": 5.0, "checkingtype": "absdiff", "answersimplification": "all", "marks": 1.0, "answer": "{f*d-b*g}/{g*a-f*c}", "checkvariablenames": false, "type": "jme"}], "steps": [{"prompt": "<p>A video example worked through. The method in the video is slightly different from the method in the solution.</p>\n          <p><iframe width=\"640\" height=\"480\" src=\"https://player.vimeo.com/video/8173488\" frameborder=\"0\"></iframe></p>", "type": "information", "marks": 0.0}], "marks": 0.0, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following linear equation for $x$.</p>\n    <p>&nbsp;</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"a": {"definition": "random(-12..12)", "name": "a"}, "c": {"definition": "if(a*g=tc*f,tc+1,tc)", "name": "c"}, "b": {"definition": "s2*random(1..12)", "name": "b"}, "d": {"definition": "if(b=td,td+1,td)", "name": "d"}, "g": {"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))", "name": "g"}, "f": {"definition": "random(1..5)", "name": "f"}, "s3": {"definition": "random(1,-1)", "name": "s3"}, "s2": {"definition": "random(1,-1)", "name": "s2"}, "s1": {"definition": "random(1,-1)", "name": "s1"}, "td": {"definition": "random(1..20)", "name": "td"}, "tc": {"definition": "s3*random(2..20)", "name": "tc"}}, "metadata": {"notes": "\n                                            \t\t    \t\t<p><strong>5/08/2012:</strong></p>\n                                            \t\t    \t\t    <p>Added more tags.</p>\n                                            \t\t    \t\t    <p>Added description.</p>\n                                            \t\t    \t\t    <p>Checked calculation. OK.</p>\n                                            \t\t    \n                                            \t\t", "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>", "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/"}]}