// Numbas version: exam_results_page_options {"name": "Lina's copy of Algebra VI: Solving Linear Equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "name": "Lina's copy of Algebra VI: Solving Linear Equation", "extensions": [], "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", "v", "n1", "n2", "n_answer"], "tags": [], "parts": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{c-b}/{a}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{c-b}/{a}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

 $\\var{a}x+\\var{b}=\\var{c}$

\n

$x=$ [[0]].

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{d-g}/{f}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{d-g}/{f}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

$\\var{d}-\\var{f}y=\\var{g}$

\n

$y=$ [[0]].

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{ans3}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{ans3}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}=\\var{k}$

\n

$z=$ [[0]]

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{ans4}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{ans4}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}=\\var{n}$.

\n

$a=$ [[0]]

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{p-r*q}/{q}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{p-r*q}/{q}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "stepsPenalty": 0, "prompt": "

$\\var{p}=\\var{q}(\\var{r}+b)$.

\n

$b=$ [[0]]

", "type": "gapfill", "showCorrectAnswer": true, "steps": [{"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

For equations of this type, it would be wise to divide the coefficient of the brackets on both sides and then rearrange as the subject variable $b$ is within the brackets.

\n

For example,

\n

Take the equation:    $5=2(1+b)$

\n

Both sides are divided by the coefficient of the brackets:    $\\frac{5}{2}=1+b$

\n

Thequation is then rearranged in a typical manner to make $b$ the subject and is simplified:    $b=\\frac{5}{2}-1=\\frac{3}{2}$

", "type": "information", "showCorrectAnswer": true}], "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "customMarkingAlgorithm": "", "unitTests": [], "maxValue": "{u*t}/{s}", "customName": "", "showCorrectAnswer": true, "marks": 1, "correctAnswerFraction": false, "correctAnswerStyle": "plain", "strictPrecision": false, "type": "numberentry", "showPrecisionHint": false, "precision": "2", "useCustomName": false, "mustBeReduced": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "mustBeReducedPC": 0, "scripts": {}, "showFeedbackIcon": true, "variableReplacements": [], "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "precisionType": "dp", "minValue": "{u*t}/{s}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}=\\var{u}$.

\n

$w=$ [[0]]

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}, {"marks": 0, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "gaps": [{"marks": 1, "allowFractions": false, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "maxValue": "{n_answer}", "customName": "", "variableReplacements": [], "useCustomName": false, "mustBeReducedPC": 0, "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "correctAnswerStyle": "plain", "mustBeReduced": false, "type": "numberentry", "showCorrectAnswer": true, "minValue": "{n_answer}"}], "customMarkingAlgorithm": "", "scripts": {}, "showFeedbackIcon": true, "unitTests": [], "customName": "", "variableReplacements": [], "useCustomName": false, "prompt": "

$\\var{n1}+\\var{n2}=$[[0]].

", "type": "gapfill", "showCorrectAnswer": true, "sortAnswers": false}], "variables": {"p": {"description": "", "name": "p", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12 except[0,q])"}, "g": {"description": "", "name": "g", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12 except [0])"}, "k": {"description": "", "name": "k", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-13..-1 except -j)"}, "t": {"description": "", "name": "t", "templateType": "anything", "group": "Ungrouped variables", "definition": "random([13,11,7,5,3,2] except s)"}, "q": {"description": "", "name": "q", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,1,-1])"}, "ans5": {"description": "", "name": "ans5", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround((p/q-r),2)"}, "ans1": {"description": "", "name": "ans1", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(((c-b)/a),2)"}, "j": {"description": "", "name": "j", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12 except [h])"}, "f": {"description": "", "name": "f", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)"}, "c": {"description": "", "name": "c", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12 except [0,b])"}, "m": {"description": "", "name": "m", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12 except l)"}, "n_answer": {"description": "", "name": "n_answer", "templateType": "anything", "group": "Ungrouped variables", "definition": "n1+n2"}, "r": {"description": "", "name": "r", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..12)"}, "ans4": {"description": "", "name": "ans4", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround((n*m+l),2)"}, "d": {"description": "", "name": "d", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..12 except [f,g])"}, "a": {"description": "", "name": "a", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)"}, "h": {"description": "", "name": "h", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(list(2..12)+[20,50,100,200])"}, "b": {"description": "", "name": "b", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12 except a)"}, "l": {"description": "", "name": "l", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(2..12)"}, "ans3": {"description": "", "name": "ans3", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(((k+j)*h,2))"}, "ans2": {"description": "", "name": "ans2", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(((g-d)/(-f),2))"}, "s": {"description": "", "name": "s", "templateType": "anything", "group": "Ungrouped variables", "definition": "random([-13,-11,-7,-5,-3,-2,13,11,7,5,3,2])"}, "n": {"description": "", "name": "n", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12)"}, "n2": {"description": "", "name": "n2", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-15..15 except n1)"}, "v": {"description": "", "name": "v", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround(({p-r*q})/{q},2)"}, "n1": {"description": "", "name": "n1", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(1..4)"}, "ans6": {"description": "", "name": "ans6", "templateType": "anything", "group": "Ungrouped variables", "definition": "precround((u*t/s),2)"}, "u": {"description": "", "name": "u", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(-12..12 except 0)"}}, "preamble": {"css": "", "js": ""}, "rulesets": {}, "variable_groups": [], "variablesTest": {"condition": "", "maxRuns": "100"}, "statement": "

Solve the following linear equations using basic BIDMAS calculations ( Answer in two decimal places only)

\n

For help on solving linear equations, check this video- https://www.youtube.com/watch?v=8j3kRdiRjPA

", "advice": "

a) Given $\\var{a}x+\\var{b}=\\var{c}$, we can start by subtracting $\\var{b}$ from both sides to get $\\var{a}x = \\simplify{{c-b}}$.

\n

Dividing both sides by $\\var{a}$ gives us $x= \\var{ans1}$

\n\n\n\n\n\n\n\n\n
\n\n\n\n\n\n\n\n\n
\n\n\n\n\n\n\n\n\n
\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
\n

b) We could start by subtracting $\\var{d}$ from both sides to get $-\\var{f}y = \\simplify{{g-d}}$.

\n

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.

\n

Either way we should end up with $y= \\dfrac{\\simplify{{d- g}}}{\\var{f}}= \\var{ans2}$

\n

\n

c)

\n

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{z}{\\var{h}}}-\\var{j}$$=$$\\var{k}$ 
 
 
$\\displaystyle{\\frac{z}{\\var{h}}}$$=$$\\var{k+j}$
 
 
$z$$=$$\\var{ans3}$
\n

d)

\n

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{a-\\var{l}}{\\var{m}}}$$=$$\\var{n}$ 
 
$a-\\var{l}$$=$$\\var{n*m}$
 
 
$a$$=$$\\var{ans4}$
\n

e)

\n

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\var{p}$$=$$\\var{q}(\\var{r}+b)$ 
 
 
$\\displaystyle{\\simplify{{p}/{q}}}$$=$$\\var{r}+b$
 
 
$\\displaystyle{\\simplify{{p-r*q}/{q}}}$$=$$b$
$\\var{ans5}$$=$$b$
\n

f)

\n

\n

\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
$\\displaystyle{\\frac{\\var{s}w}{\\var{t}}}$$=$$\\var{u}$ 
 
 
$\\var{s}w$$=$$\\var{u*t}$
 
 
\n

$w$

\n
$=$\n

$ \\var{ans6}$

\n
\n

\n

For more help, check this video- 

\n

                                               

\n

\n

", "metadata": {"description": "

This exercise will help you solve equations of type ax-b = c.

\n

", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}, {"name": "Lina van Hunen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3414/"}]}]}], "contributors": [{"name": "Nasir Firoz Khan", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/909/"}, {"name": "Lina van Hunen", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3414/"}]}