// Numbas version: finer_feedback_settings
{"name": "Rachel's copy of 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": [{"variables": {"ans4": {"templateType": "anything", "definition": "n*m+l", "description": "", "group": "Ungrouped variables", "name": "ans4"}, "f": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "f"}, "q": {"templateType": "anything", "definition": "random(-12..12 except [0,1,-1])", "description": "", "group": "Ungrouped variables", "name": "q"}, "p": {"templateType": "anything", "definition": "random(-12..12 except[0,q])", "description": "", "group": "Ungrouped variables", "name": "p"}, "ans3": {"templateType": "anything", "definition": "(k+j)*h", "description": "", "group": "Ungrouped variables", "name": "ans3"}, "r": {"templateType": "anything", "definition": "random(1..12)", "description": "", "group": "Ungrouped variables", "name": "r"}, "m": {"templateType": "anything", "definition": "random(2..12 except l)", "description": "", "group": "Ungrouped variables", "name": "m"}, "s": {"templateType": "anything", "definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])", "description": "", "group": "Ungrouped variables", "name": "s"}, "l": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "l"}, "g": {"templateType": "anything", "definition": "random(-12..12 except [0])", "description": "", "group": "Ungrouped variables", "name": "g"}, "b": {"templateType": "anything", "definition": "random(2..12 except a)", "description": "", "group": "Ungrouped variables", "name": "b"}, "ans6": {"templateType": "anything", "definition": "u*t/s", "description": "", "group": "Ungrouped variables", "name": "ans6"}, "a": {"templateType": "anything", "definition": "random(2..12)", "description": "", "group": "Ungrouped variables", "name": "a"}, "n": {"templateType": "anything", "definition": "random(-12..12)", "description": "", "group": "Ungrouped variables", "name": "n"}, "ans2": {"templateType": "anything", "definition": "(g-d)/(-f)", "description": "", "group": "Ungrouped variables", "name": "ans2"}, "c": {"templateType": "anything", "definition": "random(-12..12 except [0,b])", "description": "", "group": "Ungrouped variables", "name": "c"}, "ans5": {"templateType": "anything", "definition": "p/q-r", "description": "", "group": "Ungrouped variables", "name": "ans5"}, "j": {"templateType": "anything", "definition": "random(2..12 except [h])", "description": "", "group": "Ungrouped variables", "name": "j"}, "t": {"templateType": "anything", "definition": "random([13,11,7,5,3,2] except s)", "description": "", "group": "Ungrouped variables", "name": "t"}, "k": {"templateType": "anything", "definition": "random(-13..-1 except -j)", "description": "", "group": "Ungrouped variables", "name": "k"}, "u": {"templateType": "anything", "definition": "random(-12..12 except 0)", "description": "", "group": "Ungrouped variables", "name": "u"}, "ans1": {"templateType": "anything", "definition": "(c-b)/a", "description": "", "group": "Ungrouped variables", "name": "ans1"}, "d": {"templateType": "anything", "definition": "random(1..12 except [f,g])", "description": "", "group": "Ungrouped variables", "name": "d"}, "h": {"templateType": "anything", "definition": "random(list(2..12)+[20,50,100,200])", "description": "", "group": "Ungrouped variables", "name": "h"}}, "functions": {}, "tags": [], "statement": "<p>Solve the following equations for x:</p>", "variablesTest": {"maxRuns": "100", "condition": ""}, "preamble": {"js": "", "css": ""}, "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"], "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}}}$</p>\n<p></p>\n<p><br/>For more help, check this video-&nbsp;</p>\n<p>&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;<iframe width=\"500\" height=\"375\" src=\"//www.youtube.com/embed/9PqygqYo0ck\"></iframe></p>\n<p></p>\n<p></p>", "parts": [{"stepsPenalty": 0, "marks": 0, "prompt": "<p>&nbsp;$\\var{a}x+\\var{b}=\\var{c}$</p>\n<p>$x=$&nbsp;[[0]].</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans1}", "type": "numberentry", "scripts": {}, "strictPrecision": false, "maxValue": "{ans1}", "precisionType": "dp", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "precision": "2", "showFeedbackIcon": true, "precisionPartialCredit": 0, "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision."}], "steps": [{"marks": 1, "prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>\n<hr/>\n<p></p>\n<p>Example: &nbsp;&nbsp;<i>5 x </i>- 6 = 3<i> x</i> - 8</p>\n<p>Subtract 3x from both sides of the equation: 2x - 6 = -8</p>\n<p>Add 6 to both sides of the equation: 2x = -2 or x= -1</p>\n<p></p>\n<p></p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "extension", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "<p>$\\var{d}-\\var{f}y=\\var{g}$</p>\n<p>$y=$&nbsp;[[0]].</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans2}", "type": "numberentry", "scripts": {}, "strictPrecision": false, "maxValue": "{ans2}", "precisionType": "dp", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "precision": "2", "showFeedbackIcon": true, "precisionPartialCredit": 0, "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision."}], "steps": [{"marks": 0, "prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "<p>$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$</p>\n<p>$z=$&nbsp;[[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans3}", "type": "numberentry", "scripts": {}, "maxValue": "{ans3}", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false}], "steps": [{"marks": 0, "prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "<p>$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$.</p>\n<p>$a=$&nbsp;[[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "minValue": "{ans4}", "type": "numberentry", "scripts": {}, "maxValue": "{ans4}", "mustBeReducedPC": 0, "allowFractions": true, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "showFeedbackIcon": true, "mustBeReduced": false}], "steps": [{"marks": 0, "prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "<p>$\\var{p}=\\var{q}(\\var{r}+b)$.</p>\n<p>$b=$&nbsp;[[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{p-r*q}/{q}", "type": "numberentry", "scripts": {}, "strictPrecision": true, "maxValue": "{p-r*q}/{q}", "precisionType": "dp", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "precision": "2", "showFeedbackIcon": true, "precisionPartialCredit": 0, "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision."}], "steps": [{"marks": 0, "prompt": "<ul>\n<li><b>In order to solve for the unknown variable, you must isolate the variable.</b></li>\n<li style=\"text-align: left;\"><b>In the order of operation, multiplication and division are completed before addition and subtraction.</b></li>\n</ul>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}, {"stepsPenalty": 0, "marks": 0, "prompt": "<p>$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.</p>\n<p>$w=$&nbsp;[[0]]</p>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "gapfill", "scripts": {}, "gaps": [{"marks": 1, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "showPrecisionHint": true, "notationStyles": ["plain", "en", "si-en"], "minValue": "{u*t}/{s}", "type": "numberentry", "scripts": {}, "strictPrecision": true, "maxValue": "{u*t}/{s}", "precisionType": "dp", "mustBeReducedPC": 0, "allowFractions": false, "variableReplacements": [], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "precision": "2", "showFeedbackIcon": true, "precisionPartialCredit": 0, "mustBeReduced": false, "precisionMessage": "You have not given your answer to the correct precision."}], "steps": [{"marks": 0, "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>", "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "showFeedbackIcon": true, "type": "information", "scripts": {}}]}], "extensions": [], "variable_groups": [], "name": "Rachel's copy of Algebra VI: Solving Linear Equations (Sarah)", "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"}, "rulesets": {}, "type": "question", "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}]}], "contributors": [{"name": "Rachel Staddon", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/901/"}]}