// Numbas version: finer_feedback_settings
{"name": "44.c Division to solve an inequality", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "44.c Division to solve an inequality", "tags": [], "metadata": {"description": "<p>Solving an inequality of the form ax &lt; b</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "<p>Solve in the inequality</p>\n<p>\\[\\simplify{{a1}x}\\var{Symb[0]}\\var{a1*a2}.\\]</p>\n<p></p>", "advice": "<p>We treat inequalities similarly to solving to an equation. We want to get $x$ on its own on one side, in this case we can achieve this by dividing $\\var{a1}$ from both sides which gives us the following.</p>\n<p>\\[\\simplify{{a1}x}\\var{Symb[0]}\\var{a1*a2}\\]</p>\n<p>\\[\\simplify[!all]{{a1}x/{a1}}\\var{Symb[0]}\\simplify[!all]{{a1*a2}/{a1}}\\]</p>\n<p>\\[x\\var{Symb[0]}\\var{a2}\\]</p>\n<p></p>\n<p><a href=\"https://www.sheffield.ac.uk/mash/maths-resources/maths-all#Inequalities\"><span style=\"font-weight: 400;\">Use this link to find some resources which will help you revise this topic.</span></a></p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"a1": {"name": "a1", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "a2": {"name": "a2", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,1,-1])", "description": "", "templateType": "anything", "can_override": false}, "Symb": {"name": "Symb", "group": "Ungrouped variables", "definition": "random([latex(\"<\"),\"<\"],[latex(\">\"),\">\"],[latex(\"\\\\geq\"),\">=\"],[latex(\"\\\\leq\"),\"<=\"])", "description": "", "templateType": "anything", "can_override": false}, "Ans": {"name": "Ans", "group": "Ungrouped variables", "definition": "expression(\"x\"+Symb[1]+string(a2))", "description": "", "templateType": "anything", "can_override": false}, "AnsMatrix": {"name": "AnsMatrix", "group": "Ungrouped variables", "definition": "if(Symb[1]=SymbolOptions[x],1,0) for: x of: 0..3", "description": "", "templateType": "anything", "can_override": false}, "SymbolOptions": {"name": "SymbolOptions", "group": "Ungrouped variables", "definition": "[\"<\",\"<=\",\">\",\">=\"]", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["a1", "a2", "Symb", "Ans", "AnsMatrix", "SymbolOptions"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>x[[1]][[0]]</p>", "gaps": [{"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, "minValue": "{a2}", "maxValue": "{a2}", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "1_n_2", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minMarks": 0, "maxMarks": 0, "shuffleChoices": false, "displayType": "dropdownlist", "displayColumns": 0, "showBlankOption": true, "showCellAnswerState": true, "choices": ["&lt;", "&le;", "&gt;", "&ge;"], "matrix": "AnsMatrix"}], "sortAnswers": false}], "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/"}]}