// Numbas version: finer_feedback_settings
{"name": "Algebra VI: Solving Linear Equations (Sarah)", "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": "Algebra VI: Solving Linear Equations (Sarah)", "tags": [], "advice": "<p><span style=\"text-decoration: underline;\"><strong>Part a) </strong></span></p>\n<p>Given $\\var{a}x+\\var{b}=\\var{c}$, we can start by subtracting $\\var{b}$ from both sides to get $\\var{a}x = \\simplify{{c-b}}$.</p>\n<p>Dividing both sides by $\\var{a}$ gives us $x= \\simplify {{c-b}/{a}}$</p>\n<p></p>\n<p><br/><span style=\"text-decoration: underline;\"><strong>Part b)</strong></span></p>\n<p>We could start by subtracting&nbsp;$\\var{d}$ from both sides to get $-\\var{f}y = \\simplify{{g-d}}$.</p>\n<p>Or we could first add $\\var{f}y $ to both sides to get $\\var{d} = \\var{g} + \\var{f}y$. This avoids needing to divide by a negative number.</p>\n<p>Either way we should end up with $y= \\dfrac{\\simplify{{d- g}}}{\\var{f}}= \\simplify{{d-g}/{f}}$.</p>\n<p><strong></strong></p>\n<p><strong></strong></p>\n<p><span style=\"text-decoration: underline;\"><strong>Part c)</strong></span></p>\n<p>$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$&nbsp;</p>\n<p>$\\displaystyle{\\frac{z}{\\var{h}}}=\\var{k+j}$</p>\n<p>$z=\\var{ans3}$</p>\n<p></p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>Part d)</strong></span></p>\n<p>$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$</p>\n<p>$a-\\var{l}=\\var{n*m}$</p>\n<p>$a=\\var{ans4}$</p>\n<p><br/><br/></p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>Part e)</strong></span></p>\n<p>$\\var{p}$$=$$\\var{q}(\\var{r}+b)$&nbsp;</p>\n<p>$\\displaystyle{\\simplify{{p}/{q}}}$$=$$\\var{r}+b$</p>\n<p>$\\displaystyle{\\simplify{{p-r*q}/{q}}}$$=$$b$</p>\n<p></p>\n<p></p>\n<p><span style=\"text-decoration: underline;\"><strong>Part f)</strong></span></p>\n<p>$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$$=$$\\var{u}$&nbsp;</p>\n<p>$\\var{s}w$$=$$\\var{u*t}$</p>\n<p>$w$$=$$\\displaystyle{\\simplify{{u*t}/{s}}}$</p>\n<p></p>\n<p><br/>For more help, check this video-&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/9PqygqYo0ck\"></iframe></p>\n<p></p>\n<p></p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "prompt": "<p>&nbsp;$\\var{a}x+\\var{b}=\\var{c}$</p>\n<p>$x=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{c-b}/{a}", "minValue": "{c-b}/{a}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>\n<hr/>\n<p></p>\n<p>Example: &nbsp;&nbsp;<i>5 x </i>- 6 = 3<i> x</i> - 8</p>\n<p>Subtract 3x from both sides of the equation: 2x - 6 = -8</p>\n<p>Add 6 to both sides of the equation: 2x = -2 or x= -1</p>\n<p></p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "extension"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\var{d}-\\var{f}y=\\var{g}$</p>\n<p>$y=$&nbsp;[[0]].</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{d-g}/{f}", "minValue": "{d-g}/{f}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$</p>\n<p>$z=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": false, "variableReplacements": [], "maxValue": "{ans3}", "minValue": "{ans3}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{ans4}", "minValue": "{ans4}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\var{p}=\\var{q}(\\var{r}+b)$.</p>\n<p>$b=$&nbsp;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"allowFractions": true, "variableReplacements": [], "maxValue": "{p-r*q}/{q}", "minValue": "{p-r*q}/{q}", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": true, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}, {"stepsPenalty": 0, "prompt": "<p>$\\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": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "<p>Solve the following linear equations using basic BIDMAS calculations:</p>\n<p>For help on solving linear equations, check this video-&nbsp;<a href=\"https://www.youtube.com/watch?v=8j3kRdiRjPA\">https://www.youtube.com/watch?v=8j3kRdiRjPA</a></p>\n<p>Give your answer as either an integer, a non-recurring decimal or a fraction</p>", "variable_groups": [], "variablesTest": {"maxRuns": "100", "condition": ""}, "preamble": {"css": "", "js": ""}, "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(2..12)", "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(2..12)", "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..-1 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": {"description": "<p>This exercise will help you solve equations of type ax-b = c.</p>\n<p></p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}]}], "contributors": [{"name": "Sarah Turner", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/881/"}]}