// Numbas version: exam_results_page_options {"name": "David's copy of Rachel's copy of Algebra : Solving Linear Equations (basic)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"advice": "

In part a)

$\\simplify{x+{b[0]}={c[0]}}$

On isolating $x$ to one side,

$x= \\var{c[0]}-\\var{b[0]}$

$x= \\var{d}$

In part b)

$\\simplify{{a[1]}x={c[1]}}$

Solve for $x$,

$x= \\frac{\\var{c[1]}}{\\var{a[1]}}$

$x= \\var{f}$

In part c)

$\\simplify{{a[2]}/{af}x={c[2]}}$

$x= \\frac{\\var{c[2]}*\\var{af}}{\\var{a[2]}}$

$x= \\var{g}$

The video below explains how to carry out similar problems.

", "functions": {}, "parts": [{"variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\simplify{x+{b[0]}={c[0]}}$

$x=$ [[0]]

", "scripts": {}, "marks": 0, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxValue": "{c[0]}-{b[0]}", "minValue": "{c[0]}-{b[0]}", "marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "showFeedbackIcon": true, "notationStyles": ["plain", "en", "si-en"], "variableReplacements": [], "scripts": {}, "allowFractions": false, "type": "numberentry"}]}, {"variableReplacementStrategy": "originalfirst", "type": "gapfill", "showCorrectAnswer": true, "showFeedbackIcon": true, "prompt": "

$\\simplify{{a[1]}x={c[1]}}$

$x=$ [[0]]

", "scripts": {}, "marks": 0, "variableReplacements": [], "gaps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxValue": "{c[1]}/{a[1]}", "minValue": "{c[1]}/{a[1]}", "marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": true, "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precision": "2", "precisionType": "dp", "scripts": {}, "allowFractions": false, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "type": "numberentry"}]}, {"variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "showCorrectAnswer": true, "prompt": "

When the coefficient of $x$ is a fraction, you follow the same steps but have to consider how we divide by a fraction.

For example,

We start with: $\\frac{3}{4}x=6$

We 'divide both sides' by the coefficient of $x$: $\\frac{\\frac{3}{4}x}{\\frac{3}{4}}=\\frac{6}{\\frac{3}{4}}$

The coefficient of $x$ cancels: $x=\\frac{6}{\\frac{3}{4}}$

Now, to divide $6$ by $\\frac{3}{4}$, you can also multipliy $6$ by the fraction reciprocal (flipped): $x=6\\times\\frac{4}{3}$

When simplified, we're left with the final answer: $x=8$

", "scripts": {}, "marks": 0, "variableReplacements": [], "type": "information"}], "showCorrectAnswer": true, "stepsPenalty": 0, "prompt": "

$\\simplify{{a[2]}/{af}x={c[2]}}$

$x=$ [[0]]

", "variableReplacements": [], "scripts": {}, "marks": 0, "showFeedbackIcon": true, "gaps": [{"variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "maxValue": "{c[2]}{af}/{a[2]}", "minValue": "{c[2]}{af}/{a[2]}", "marks": 1, "correctAnswerStyle": "plain", "correctAnswerFraction": false, "variableReplacements": [], "showPrecisionHint": true, "precisionPartialCredit": 0, "notationStyles": ["plain", "en", "si-en"], "showFeedbackIcon": true, "precision": "2", "precisionType": "dp", "scripts": {}, "allowFractions": false, "precisionMessage": "You have not given your answer to the correct precision.", "strictPrecision": false, "type": "numberentry"}], "type": "gapfill"}], "extensions": [], "variable_groups": [], "statement": "

Find $x$ in the following equations. Give your answer correct to two decimal places when the answer isn't a whole number.

", "ungrouped_variables": ["a", "af", "b", "c", "d", "f", "g"], "name": "David's copy of Rachel's copy of Algebra : Solving Linear Equations (basic)", "rulesets": {}, "metadata": {"description": "

Basic solving of linear equations.

", "licence": "Creative Commons Attribution 4.0 International"}, "variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"css": "", "js": ""}, "variables": {"b": {"name": "b", "description": "

constant on lhs

", "group": "Ungrouped variables", "definition": "repeat(random(-10..10 except 0 except 1 except 2 except -1 except -2 except 6 except -6),3)", "templateType": "anything"}, "c": {"name": "c", "description": "

constant on rhs

", "group": "Ungrouped variables", "definition": "repeat(random(5..15 except 14 except 12 except 7),3)", "templateType": "anything"}, "af": {"name": "af", "description": "

coefficient denominator

", "group": "Ungrouped variables", "definition": "random(2..6 except a)", "templateType": "anything"}, "g": {"name": "g", "description": "", "group": "Ungrouped variables", "definition": "precround(((c[2]*{af})/a[2]),2)", "templateType": "anything"}, "a": {"name": "a", "description": "

coefficient of x on lhs

", "group": "Ungrouped variables", "definition": "repeat(random(3..6),3)", "templateType": "anything"}, "d": {"name": "d", "description": "", "group": "Ungrouped variables", "definition": "c[0]-b[0]", "templateType": "anything"}, "f": {"name": "f", "description": "", "group": "Ungrouped variables", "definition": "precround((c[1]/a[1]),2)", "templateType": "anything"}}, "tags": [], "type": "question", "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}]}], "contributors": [{"name": "David Wishart", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1461/"}]}