// Numbas version: exam_results_page_options
{"name": "Solving linear inequalities/inequations: two inequalities", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"rulesets": {}, "preamble": {"js": "", "css": ""}, "tags": ["algebra", "balancing equations", "inequalities", "inequality", "inequation", "inequations", "Linear equations", "linear equations", "rearranging equations", "solving equations", "Solving equations", "two step equations"], "ungrouped_variables": ["a", "b", "c", "left_ba", "right_ba", "left_bb", "right_bb", "left_bc", "right_bc", "bleft", "bright"], "question_groups": [{"pickingStrategy": "all-ordered", "questions": [], "pickQuestions": 0, "name": ""}], "advice": "", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": ""}, "parts": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Given that $x&gt;\\var{left_ba}$ and $x&lt;\\var{right_ba}$, we can write&nbsp;[[0]] $&lt;x&lt;$&nbsp;[[1]].</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{left_ba}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{left_ba}"}, {"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{right_ba}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{right_ba}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>$\\var{left_ba} &lt;x&lt; \\var{right_ba}$ means $\\var{left_ba} &lt;x$ and $x&lt; \\var{right_ba}$. You could read this as \"$x$ is between&nbsp;$\\var{left_ba}$ and $\\var{right_ba}$\".</p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>Given $\\var{left_bb}&lt;\\frac{x}{\\var{c}}&lt;\\var{right_bb}$, solving for $x$ gives&nbsp;[[0]]$&lt;x&lt;$&nbsp;[[1]].</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{bleft}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{bleft}"}, {"allowFractions": false, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": false, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{bright}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{bright}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Solving inequalities is similar to solving equations, ensure you do the same thing to <em>all</em> sides.&nbsp;Note that the operations we do are to get $x$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bb}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\displaystyle \\frac{x}{\\var{c}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bb}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bb}\\times \\var{c}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\displaystyle \\frac{x}{\\var{c}}\\times \\var{c}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bb}\\times \\var{c}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{bleft}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{bright}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}, {"scripts": {}, "variableReplacements": [], "prompt": "<p>Given $\\var{left_bc}&lt;\\frac{\\simplify{{a}x+{b}}}{\\var{c}}&lt;\\var{right_bc}$, solving for $x$ gives&nbsp;[[0]]$&lt;x&lt;$&nbsp;[[1]].</p>", "stepsPenalty": "1", "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{left_bc*c-b}/{a}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{left_bc*c-b}/{a}"}, {"allowFractions": true, "variableReplacements": [], "type": "numberentry", "correctAnswerFraction": true, "variableReplacementStrategy": "originalfirst", "marks": 1, "showCorrectAnswer": true, "minValue": "{right_bc*c-b}/{a}", "scripts": {}, "showPrecisionHint": false, "maxValue": "{right_bc*c-b}/{a}"}], "showCorrectAnswer": true, "marks": 0, "type": "gapfill", "steps": [{"scripts": {}, "variableReplacements": [], "prompt": "<p>Solving inequalities is similar to solving equations, ensure you do the same thing to <em>all</em> sides. Note that the operations we do are to get $x$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bc}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\displaystyle \\frac{\\simplify{{a}x+{b}}}{\\var{c}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bc}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bc}\\times \\var{c}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\displaystyle \\frac{\\simplify{{a}x+{b}}}{\\var{c}}\\times \\var{c}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bc}\\times \\var{c}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bc*c}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\simplify{{a}x+{b}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bc*c}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\simplify[basic]{{left_bc*c}-{b}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\simplify[basic]{{a}x+{b}-{b}}$</td>\n<td style=\"text-align: center;\">&nbsp;$&lt;$</td>\n<td style=\"text-align: left;\">$\\simplify[basic]{{right_bc*c}-{b}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{left_bc*c-b}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\var{a}x$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\var{right_bc*c-b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle\\frac{\\var{left_bc*c-b}}{\\var{a}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$\\displaystyle\\frac{\\var{a}x}{\\var{a}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\displaystyle\\frac{\\var{right_bc*c-b}}{\\var{a}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: center;\">&nbsp;</td>\n<td style=\"text-align: center;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle\\simplify{{left_bc*c-b}/{a}}$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: center;\">$x$</td>\n<td style=\"text-align: center;\">$&lt;$</td>\n<td style=\"text-align: left;\">$\\displaystyle\\simplify{{right_bc*c-b}/{a}}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>", "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "marks": 0, "type": "information"}]}], "showQuestionGroupNames": false, "statement": "", "variables": {"c": {"description": "", "group": "Ungrouped variables", "name": "c", "definition": "random(2..12)", "templateType": "anything"}, "left_ba": {"description": "", "group": "Ungrouped variables", "name": "left_ba", "definition": "random(-12..2)", "templateType": "anything"}, "a": {"description": "", "group": "Ungrouped variables", "name": "a", "definition": "random(2..12)", "templateType": "anything"}, "b": {"description": "", "group": "Ungrouped variables", "name": "b", "definition": "random(-12..12 except [-1,0,1])", "templateType": "anything"}, "left_bc": {"description": "", "group": "Ungrouped variables", "name": "left_bc", "definition": "random(-12..2)", "templateType": "anything"}, "right_ba": {"description": "", "group": "Ungrouped variables", "name": "right_ba", "definition": "left_ba+random(2..10)", "templateType": "anything"}, "bleft": {"description": "", "group": "Ungrouped variables", "name": "bleft", "definition": "left_bb*c", "templateType": "anything"}, "left_bb": {"description": "", "group": "Ungrouped variables", "name": "left_bb", "definition": "random(-12..2)", "templateType": "anything"}, "right_bb": {"description": "", "group": "Ungrouped variables", "name": "right_bb", "definition": "left_bb+random(2..10)", "templateType": "anything"}, "right_bc": {"description": "", "group": "Ungrouped variables", "name": "right_bc", "definition": "left_bc+random(2..10)", "templateType": "anything"}, "bright": {"description": "", "group": "Ungrouped variables", "name": "bright", "definition": "right_bb*c", "templateType": "anything"}}, "metadata": {"description": "", "notes": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "functions": {}, "name": "Solving linear inequalities/inequations: two inequalities", "type": "question", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}, {"name": "Xiaodan Leng", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2146/"}]}