// Numbas version: finer_feedback_settings
{"name": "37.e Simple linear equations 5 - Addition and multiplication", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "37.e Simple linear equations 5 - Addition and multiplication", "tags": [], "metadata": {"description": "<p>Solving two step linear equations including a division.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Solve the following equation for $\\var{Letter}$.</p>\n<p>\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}.\\]</p>", "advice": "<p>To solve $\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}$ we need to get the $\\var{Letter}$ by itself. It is easiest if we subtract $\\var{Num2}$ from both sides first but it would also be ok to multiply both sides by $\\var{Num1}$ so long as we remember to multiply both $\\simplify[basic]{{Letter}/{Num1}}$ and $\\var{Num2}$. Starting by subtracting $\\var{Num2}$ from both sides we get the following.</p>\n<p>\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}}=\\var{Num3}\\]</p>\n<p>\\[\\simplify[basic]{{Letter}/{Num1}+{Num2}-{Num2}}=\\simplify[basic]{{Num3}-{Num2}}\\]</p>\n<p>\\[\\simplify[basic]{{Letter}/{Num1}}=\\var{Num3-Num2}\\]</p>\n<p>\\[\\simplify[basic]{{Letter}/{Num1}}\\times \\var{Num1}=\\var{Num3-Num2}\\times\\var{Num1}\\]</p>\n<p>\\[\\var{Letter}=\\var{(Num3-Num2)*Num1}.\\]</p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Equations\" target=\"_blank\" rel=\"noopener\"><br/>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..10)", "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(-12..12 except 0)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "abs(Num3-Num2)<13", "maxRuns": 100}, "ungrouped_variables": ["Letter", "Num1", "Num2", "Num3"], "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": "{Num1*(Num3-Num2)}", "maxValue": "{Num1*(Num3-Num2)}", "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/"}]}