// Numbas version: finer_feedback_settings {"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": [{"preamble": {"css": "", "js": ""}, "variables": {"q": {"templateType": "anything", "definition": "random(-12..12 except [0,1,-1])", "name": "q", "group": "Ungrouped variables", "description": ""}, "t": {"templateType": "anything", "definition": "random([13,11,7,5,3,2] except s)", "name": "t", "group": "Ungrouped variables", "description": ""}, "ans3": {"templateType": "anything", "definition": "(k+j)*h", "name": "ans3", "group": "Ungrouped variables", "description": ""}, "ans5": {"templateType": "anything", "definition": "p/q-r", "name": "ans5", "group": "Ungrouped variables", "description": ""}, "ans6": {"templateType": "anything", "definition": "u*t/s", "name": "ans6", "group": "Ungrouped variables", "description": ""}, "u": {"templateType": "anything", "definition": "random(-12..12 except 0)", "name": "u", "group": "Ungrouped variables", "description": ""}, "g": {"templateType": "anything", "definition": "random(-12..12 except [0])", "name": "g", "group": "Ungrouped variables", "description": ""}, "a": {"templateType": "anything", "definition": "random(-12..12 except [0,-1,1])", "name": "a", "group": "Ungrouped variables", "description": ""}, "r": {"templateType": "anything", "definition": "random(1..12)", "name": "r", "group": "Ungrouped variables", "description": ""}, "l": {"templateType": "anything", "definition": "random(2..12)", "name": "l", "group": "Ungrouped variables", "description": ""}, "ans1": {"templateType": "anything", "definition": "(c-b)/a", "name": "ans1", "group": "Ungrouped variables", "description": ""}, "k": {"templateType": "anything", "definition": "random(-13..0 except -j)", "name": "k", "group": "Ungrouped variables", "description": ""}, "j": {"templateType": "anything", "definition": "random(2..12 except [h])", "name": "j", "group": "Ungrouped variables", "description": ""}, "p": {"templateType": "anything", "definition": "random(-12..12 except[0,q])", "name": "p", "group": "Ungrouped variables", "description": ""}, "f": {"templateType": "anything", "definition": "random(list(2..12)+[100])", "name": "f", "group": "Ungrouped variables", "description": ""}, "h": {"templateType": "anything", "definition": "random(list(2..12)+[20,50,100,200])", "name": "h", "group": "Ungrouped variables", "description": ""}, "n": {"templateType": "anything", "definition": "random(-12..12)", "name": "n", "group": "Ungrouped variables", "description": ""}, "ans4": {"templateType": "anything", "definition": "n*m+l", "name": "ans4", "group": "Ungrouped variables", "description": ""}, "ans2": {"templateType": "anything", "definition": "(g-d)/(-f)", "name": "ans2", "group": "Ungrouped variables", "description": ""}, "b": {"templateType": "anything", "definition": "random(2..12 except a)", "name": "b", "group": "Ungrouped variables", "description": ""}, "m": {"templateType": "anything", "definition": "random(2..12 except l)", "name": "m", "group": "Ungrouped variables", "description": ""}, "c": {"templateType": "anything", "definition": "random(-12..12 except [0,b])", "name": "c", "group": "Ungrouped variables", "description": ""}, "d": {"templateType": "anything", "definition": "random(1..12 except [f,g])", "name": "d", "group": "Ungrouped variables", "description": ""}, "s": {"templateType": "anything", "definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])", "name": "s", "group": "Ungrouped variables", "description": ""}}, "advice": "", "functions": {}, "rulesets": {}, "parts": [{"extendBaseMarkingAlgorithm": true, "marks": 0, "showFeedbackIcon": true, "sortAnswers": false, "stepsPenalty": "0", "variableReplacementStrategy": "originalfirst", "prompt": "

Given $\\var{a}x+\\var{b}=\\var{c}$, solving for $x$ gives $x=$ [[0]].

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Given $\\var{a}x+\\var{b}=\\var{c}$, we can 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.

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$\\var{a}x+\\var{b}$$=$$\\var{c}$ 
 
$\\var{a}x+\\var{b}-\\var{b}$$=$$\\var{c}-\\var{b}$
 
$\\var{a}x$$=$$\\var{c-b}$
 
$\\displaystyle{\\frac{\\var{a}x}{\\var{a}}}$ $=$$\\displaystyle{\\frac{\\var{c-b}}{\\var{a}}}$
 
$x$$=$$\\displaystyle{\\simplify{{c-b}/{a}}}$
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Given $\\var{d}-\\var{f}y=\\var{g}$,  $y=$ [[0]].

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Given $\\var{d}-\\var{f}y=\\var{g}$, we can 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.

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$\\var{d}-\\var{f}y$$=$$\\var{g}$ 
 
$\\var{d}-\\var{f}y-\\var{d}$$=$$\\var{g}-\\var{d}$
 
$-\\var{f}y$$=$$\\var{g-d}$
 
$\\displaystyle{\\frac{\\var{-f}y}{\\var{-f}}}$ $=$$\\displaystyle{\\frac{\\var{g-d}}{\\var{-f}}}$
 
$y$$=$$\\displaystyle{\\simplify{{g-d}/{-f}}}$
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Rearrange $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$ to determine the value of $z$.

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$z=$ [[0]]

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Given $\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$, we add $\\var{j}$ to both sides to get $\\displaystyle{\\frac{z}{\\var{h}}}$ by itself and then multiply both sides by $\\var{h}$ to get $z$ by itself.

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$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}$$=$$\\var{k}$ 
 
$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}+\\var{j}$$=$$\\var{k}+\\var{j}$
 
$\\displaystyle{\\frac{z}{\\var{h}}}$$=$$\\var{k+j}$
 
$\\displaystyle{\\frac{z}{\\var{h}}\\times\\var{h}}$ $=$$\\var{k+j}\\times \\var{h}$
 
$z$$=$$\\var{ans3}$
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Solve $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$ for $a$.

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$a=$ [[0]]

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Given $\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$, we can multiply both sides by $\\var{m}$ to get $a-\\var{l}$ by itself and then add $\\var{l}$ to both sides to get $a$ by itself.

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$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}$$=$$\\var{n}$ 
 
$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}\\times \\var{m}$$=$$\\var{n}\\times\\var{m}$
 
$a-\\var{l}$$=$$\\var{n*m}$
 
$a-\\var{l}+\\var{l}$ $=$$\\var{n*m}+\\var{l}$
 
$a$$=$$\\var{ans4}$
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Solve $\\var{p}=\\var{q}(\\var{r}+b)$.

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$b=$ [[0]]

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Given $\\var{p}=\\var{q}(\\var{r}+b)$, we can divide both sides by $\\var{q}$ to get $\\var{r}+b$ by itself and then subtract $\\var{r}$ from both sides to get $b$ by itself.

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$\\var{p}$$=$$\\var{q}(\\var{r}+b)$ 
 
$\\displaystyle{\\frac{\\var{p}}{\\var{q}}}$$=$$\\displaystyle{\\frac{\\var{q}(\\var{r}+b)}{\\var{q}}}$
 
$\\displaystyle{\\simplify{{p}/{q}}}$$=$$\\var{r}+b$
 
$\\displaystyle{\\simplify{{p}/{q}}}-\\var{r}$ $=$$\\var{r}+b-\\var{r}$
 
$\\displaystyle{\\simplify{{p-r*q}/{q}}}$$=$$b$
 
$b$$=$$\\displaystyle{\\simplify{{p-r*q}/{q}}}$
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Solve $\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.

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$w=$ [[0]]

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Given $\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$, we can multiply both sides by $\\var{t}$ to get $\\var{s}w$ by itself and then divide both sides by $\\var{s}$ to get $w$ by itself.

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$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$$=$$\\var{u}$ 
 
$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}\\times\\var{t}$$=$$\\var{u}\\times\\var{t}$
 
$\\var{s}w$$=$$\\var{u*t}$
 
$\\displaystyle{\\frac{\\var{s}w}{\\var{s}}}$ $=$$\\displaystyle{\\frac{\\var{u*t}}{\\var{s}}}$
 
$w$$=$$\\displaystyle{\\simplify{{u*t}/{s}}}$
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