// Numbas version: exam_results_page_options
{"name": "Solving linear equations: two step", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "c", "ans1", "d", "f", "g", "ans2", "h", "j", "k", "ans3", "l", "m", "n", "ans4", "p", "q", "r", "ans5", "s", "t", "u", "ans6"], "name": "Solving linear equations: two step", "tags": ["algebra", "balancing equations", "Linear equations", "linear equations", "rearranging equations", "solving equations", "Solving equations", "two step equations"], "preamble": {"css": "", "js": ""}, "advice": "", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>Given $\\var{a}x+\\var{b}=\\var{c}$, solving for $x$ gives&nbsp;$x=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{c-b}/{a}", "minValue": "{c-b}/{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{a}x+\\var{b}=\\var{c}$, we can&nbsp;subtract $\\var{b}$ from both sides to get $\\var{a}x$ by itself, and then divide both sides by $\\var{a}$ to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}-\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}-\\var{b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c-b}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{a}x}{\\var{a}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{c-b}}{\\var{a}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{c-b}/{a}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Given $\\var{d}-\\var{f}y=\\var{g}$, &nbsp;$y=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{d-g}/{f}", "minValue": "{d-g}/{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{d}-\\var{f}y=\\var{g}$, we can&nbsp;subtract $\\var{d}$ from both sides to get $-\\var{f}y$ by itself, and then divide both sides by $-\\var{f}$ to get $y$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}-\\var{f}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}-\\var{f}y-\\var{d}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}-\\var{d}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$-\\var{f}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g-d}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{-f}y}{\\var{-f}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{g-d}}{\\var{-f}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{g-d}/{-f}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Rearrange $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$ to determine the value of $z$.</p>\n<p>$z=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$, we add $\\var{j}$ to both sides to get $\\displaystyle{\\frac{z}{\\var{h}}}$&nbsp;by itself and then multiply both sides by $\\var{h}$ to get $z$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}+\\var{j}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}+\\var{j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k+j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z}{\\var{h}}\\times\\var{h}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k+j}\\times \\var{h}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans3}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Solve $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$ for&nbsp;$a$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$, we can&nbsp;multiply&nbsp;both sides by $\\var{m}$ to get $a-\\var{l}$&nbsp;by itself and then add&nbsp;$\\var{l}$ to both sides to get $a$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}\\times \\var{m}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n}\\times\\var{m}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a-\\var{l}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n*m}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a-\\var{l}+\\var{l}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{n*m}+\\var{l}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$a$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{ans4}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Solve&nbsp;$\\var{p}=\\var{q}(\\var{r}+b)$.</p>\n<p>$b=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{p-r*q}/{q}", "minValue": "{p-r*q}/{q}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\var{p}=\\var{q}(\\var{r}+b)$, we can divide&nbsp;both sides by $\\var{q}$ to get $\\var{r}+b$&nbsp;by itself and then subtract&nbsp;$\\var{r}$ from&nbsp;both sides to get $b$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{p}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{q}(\\var{r}+b)$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{p}}{\\var{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{q}(\\var{r}+b)}{\\var{q}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p}/{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r}+b$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p}/{q}}}-\\var{r}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r}+b-\\var{r}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{p-r*q}/{q}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$b$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$b$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{p-r*q}/{q}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": "1", "prompt": "<p>Solve&nbsp;$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.</p>\n<p>$w=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{u*t}/{s}", "minValue": "{u*t}/{s}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>Given $\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$, we can multiply&nbsp;both sides by $\\var{t}$ to get $\\var{s}w$&nbsp;by itself and then divide both sides by&nbsp;$\\var{s}$ to get $w$ by itself.</p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}\\times\\var{t}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u}\\times\\var{t}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{s}w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{u*t}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{s}w}{\\var{s}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{u*t}}{\\var{s}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{u*t}/{s}}}$</td>\n</tr>\n</tbody>\n</table>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "scripts": {}, "marks": 0, "showCorrectAnswer": true, "type": "gapfill"}], "statement": "", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": ""}, "variables": {"ans1": {"definition": "(c-b)/a", "templateType": "anything", "group": "Ungrouped variables", "name": "ans1", "description": ""}, "ans2": {"definition": "(g-d)/(-f)", "templateType": "anything", "group": "Ungrouped variables", "name": "ans2", "description": ""}, "ans3": {"definition": "(k+j)*h", "templateType": "anything", "group": "Ungrouped variables", "name": "ans3", "description": ""}, "ans4": {"definition": "n*m+l", "templateType": "anything", "group": "Ungrouped variables", "name": "ans4", "description": ""}, "ans5": {"definition": "p/q-r", "templateType": "anything", "group": "Ungrouped variables", "name": "ans5", "description": ""}, "ans6": {"definition": "u*t/s", "templateType": "anything", "group": "Ungrouped variables", "name": "ans6", "description": ""}, "a": {"definition": "random(-12..12 except [0,-1,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(-12..12 except [0,b])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..12 except a)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(1..12 except [f,g])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}, "g": {"definition": "random(-12..12 except [0])", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(list(2..12)+[100])", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "h": {"definition": "random(list(2..12)+[20,50,100,200])", "templateType": "anything", "group": "Ungrouped variables", "name": "h", "description": ""}, "k": {"definition": "random(-13..0 except -j)", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "j": {"definition": "random(2..12 except [h])", "templateType": "anything", "group": "Ungrouped variables", "name": "j", "description": ""}, "m": {"definition": "random(2..12 except l)", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random(2..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "n": {"definition": "random(-12..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random(-12..12 except [0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random(-12..12 except[0,q])", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(1..12)", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(-12..12 except 0)", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random([13,11,7,5,3,2] except s)", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}}, "metadata": {"notes": "", "description": "", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}