// Numbas version: finer_feedback_settings
{"name": "38.d. Linear equations - expanding brackets needed 2", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "38.d. Linear equations - expanding brackets needed 2", "tags": [], "metadata": {"description": "<p>Solving equations of the form a(ex+b)=c(fx+d)</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Solve the following equation for $\\var{Letter}$.</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1}({Num5}{Letter}+{Num2})}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3}({Num6}{Letter} +{Num4})}.\\]</p>", "advice": "<p>To solve $\\simplify[basic,unitFactor,noLeadingMinus]{{Num1}({Num5}{Letter}+{Num2})}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3}({Num6}{Letter} +{Num4})}$ we need to expand the brackets and then get all the $\\var{Letter}$ terms on one side and all the numbers on the other.</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1}({Num5}{Letter}+{Num2})}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3}({Num6}{Letter} +{Num4})}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1}*{Num5}{Letter}+{Num1}*{Num2}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3}*{Num6}{Letter} +{Num3}*{Num4}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5}{Letter}+{Num1*Num2}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num6}{Letter} +{Num3*Num4}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5}{Letter}+{Num1*Num2}-{Num1*Num2}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num6}{Letter} +{Num3*Num4}-{Num1*Num2}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5}{Letter}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num6}{Letter}+{Num3*Num4-Num1*Num2}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5}{Letter}-{Num3*Num6}{Letter}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num6}{Letter}+{Num3*Num4-Num1*Num2}-{Num3*Num6}{Letter}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5-Num3*Num6}{Letter}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num4-Num1*Num2}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Num1*Num5-Num3*Num6}{Letter}/{Num1*Num5-Num3*Num6}}=\\simplify[basic,unitFactor,noLeadingMinus]{{Num3*Num4-Num1*Num2}/{Num1*Num5-Num3*Num6}}\\]</p>\n<p>\\[\\simplify[basic,unitFactor,noLeadingMinus]{{Letter}}=\\simplify[basic,unitFactor,noLeadingMinus]{{(Num3*Num4-Num1*Num2)/(Num1*Num5-Num3*Num6)}}\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Equations\" target=\"_blank\" rel=\"noopener\">Use this link to find resources to help you revise how to solve linear equations</a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"Letter": {"name": "Letter", "group": "Ungrouped variables", "definition": "random([\"a\",\"b\",\"c\",\"d\",\"p\",\"t\",\"s\",\"n\",\"m\",\"x\",\"y\",\"z\"])", "description": "", "templateType": "anything", "can_override": false}, "Num1": {"name": "Num1", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "Num2": {"name": "Num2", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Num3": {"name": "Num3", "group": "Ungrouped variables", "definition": "random(2..12 except Num1)", "description": "", "templateType": "anything", "can_override": false}, "Num4": {"name": "Num4", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Num5": {"name": "Num5", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}, "Num6": {"name": "Num6", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(Num1*Num5-Num3*Num6)>1 and abs(Num1*Num5-Num3*Num6)<12 and (Num1*Num5-Num3*Num6)|(Num4*Num3-Num2*Num1)", "maxRuns": "300"}, "ungrouped_variables": ["Letter", "Num1", "Num2", "Num3", "Num4", "Num5", "Num6"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>$\\var{Letter} =$</p>", "minValue": "{(Num4*Num3-Num2*Num1)/(Num1*Num5-Num3*Num6)}", "maxValue": "{(Num4*Num3-Num2*Num1)/(Num1*Num5-Num3*Num6)}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}], "resources": []}]}], "contributors": [{"name": "Mash Sheffield", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4679/"}, {"name": "Andrew Neate", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/21832/"}]}