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{"name": "Solve a linear equation $ax+b = c$", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Solve a linear equation of the form $ax+b = c$, where $a$, $b$ and $c$ are integers.</p>\n<p>The answer is always an integer.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "ungrouped_variables": [], "type": "question", "rulesets": {}, "advice": "<p>We need to solve the equation</p>\n<p>\\[ \\var{a}x+\\var{b}=\\var{c} \\]</p>\n<p>To solve this equation, we must rearrange the equation to put $x$ on its own.</p>\n<p>To do this, we should subtract $\\var{b}$ from both sides and then divide through by $\\var{a}$ to get the value for $x$.</p>\n<p>\\begin{align}<br/>\\var{a}x+\\var{b}&amp;=\\var{c} \\\\[0.5em]<br/>\\var{a}x&amp;=\\var{c}-\\var{b} &amp; \\text{Subtract } \\var{b} \\text{ from both sides} \\\\[0.5em]<br/>\\var{a}x&amp;=\\var{c-b} \\\\[0.5em]<br/>x&amp;=\\frac{\\var{c-b}}{\\var{a}} &amp; \\text{Divide both sides by } \\var{a} \\\\[0.5em]<br/>x&amp;=\\simplify{{c-b}/{a}}<br/>\\end{align}</p>\n<p style=\"text-align: left;\"></p>", "variables": {"b": {"description": "", "definition": "random(1..15)", "group": "part a", "name": "b", "templateType": "anything"}, "c": {"description": "", "definition": "(x*a)+b", "group": "part a", "name": "c", "templateType": "anything"}, "a": {"description": "", "definition": "random(2..10)", "group": "part a", "name": "a", "templateType": "anything"}, "x": {"description": "", "definition": "random(2..6)", "group": "part a", "name": "x", "templateType": "anything"}}, "statement": "", "name": "Solve a linear equation $ax+b = c$", "parts": [{"scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "prompt": "<p>$\\var{a}x+\\var{b}=\\var{c}$</p>\n<p>What is the value of $x$?</p>\n<p>$x = $ [[0]]</p>", "variableReplacements": [], "showFeedbackIcon": true, "marks": 0, "gaps": [{"correctAnswerFraction": false, "showCorrectAnswer": true, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "allowFractions": false, "minValue": "x", "scripts": {}, "variableReplacementStrategy": "originalfirst", "type": "numberentry", "maxValue": "x", "mustBeReduced": false, "marks": "2", "variableReplacements": [], "correctAnswerStyle": "plain", "mustBeReducedPC": 0}]}], "tags": ["linear equation", "linear equations", "Linear equations", "solving linear equations", "taxonomy"], "preamble": {"js": "", "css": ""}, "variable_groups": [{"name": "part a", "variables": ["a", "b", "c", "x"]}], "functions": {}, "extensions": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Lauren Richards", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1589/"}]}