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{"name": "AC1 Solve linear equations", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "AC1 Solve linear equations", "tags": [], "metadata": {"description": "<p>Solve linear equations with unkowns on both sides. Including brackets and fractions.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "<p>Given $\\simplify{{m}w-{n} = {p}w+{q}}$, we can get all the $w$'s on the left hand side and all the numbers on the right hand side, and then divide both sides by the coefficient of $w$ to get $w$ by itself.</p>\n<p></p>\n<table style=\"height: 342px;\">\n<tbody>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\simplify{{m}w+{n}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\simplify{{p}w+{q}}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">&nbsp;</td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\"></td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\simplify[!cancelTerms,unitFactor]{{m}w-{n}-{p}w}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\simplify{{m-p}w-{n}}$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\var{m-p}w-\\var{n}+\\var{n}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\var{q}+\\var{n}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\">$\\var{m-p}w$</td>\n<td style=\"height: 18px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">$\\var{q+n}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$\\displaystyle{\\frac{\\var{m-p}w}{\\var{m-p}}}$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\frac{\\var{q+n}}{\\var{m-p}}}$</td>\n</tr>\n<tr style=\"height: 18px;\">\n<td style=\"text-align: right; height: 18px; width: 218.312px;\"></td>\n<td style=\"height: 18px; width: 29.2656px;\"></td>\n<td style=\"text-align: left; height: 18px; width: 283.422px;\">&nbsp;</td>\n</tr>\n<tr style=\"height: 36px;\">\n<td style=\"text-align: right; height: 36px; width: 218.312px;\">$w$</td>\n<td style=\"height: 36px; width: 29.2656px;\">$=$</td>\n<td style=\"text-align: left; height: 36px; width: 283.422px;\">$\\displaystyle{\\simplify{{q+n}/{m-p}}} = \\var{precround(ansA,1)} \\text{ to 1 dp}$</td>\n</tr>\n</tbody>\n</table>\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}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1..3)", "description": "", "templateType": "anything", "can_override": false}, "m": {"name": "m", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "q": {"name": "q", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "random(1..12)", "description": "", "templateType": "anything", "can_override": false}, "l": {"name": "l", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "ansA": {"name": "ansA", "group": "Ungrouped variables", "definition": "(q+n)/(m-p)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "100"}, "ungrouped_variables": ["l", "m", "n", "p", "q", "ansA"], "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>Solve&nbsp; 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