// Numbas version: finer_feedback_settings
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"exploreObjective": null, "prompt": "<p>We can solve&nbsp;$\\var{a}x+\\var{b}=\\var{c}x$ by collecting like terms and rearranging&nbsp;for $x$.</p>\n<p>This gives&nbsp;$x=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\var{a}x+\\var{b}=\\var{c}x$, we can&nbsp;subtract $\\var{a}x$ from both sides to collect like terms, and then divide both sides by the coefficient of $x$&nbsp;to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}x$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{a}x+\\var{b}-\\var{a}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c}x-\\var{a}x$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{b}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{c-a}x$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{b}}{\\var{c-a}}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{c-a}x}{\\var{c-a}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\simplify{{b}/{c-a}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$x$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{b}/{c-a}}}$</td>\n</tr>\n</tbody>\n</table>\n<p></p>\n<p>There is often more than one way to solve an equation, one strategy used above in the first step was to get all the $x\\text{'s}$ one the side with the most $x\\text{'s}$, that way you end up with a positive number of $x\\text{'s}$. This is not necessary, we could have put all the $x$'s on the left-hand side but notice in this question that we then would have had to move the $\\var{b}$ onto the right-hand side, so it would have required more work, but nevertheless that method would result in the same result for $x$.</p>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{-b}/{a-c}", "maxValue": "{-b}/{a-c}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve&nbsp;$\\var{l}(\\var{m}w-\\var{n})=\\var{p}w+\\var{q}$ for $w$.</p>\n<p>$w=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\var{l}(\\var{m}w-\\var{n})=\\var{p}w+\\var{q}$, we can expand the brackets, get all the $w\\text{'s}$ on the left-hand side, collect like terms, get all the numbers on the right-hand side, collect like terms and then divide both sides by the coefficient of $w$ to get $w$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\var{l}(\\var{m}w-\\var{n})$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{p}w+\\var{q}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{l*m}w-\\var{n*l}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{p}w+\\var{q}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{l*m}w-\\var{n*l}-\\var{p}w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{p}w+\\var{q}-\\var{p}w$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{l*m-p}w-\\var{n*l}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{q}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{l*m-p}w-\\var{n*l}+\\var{n*l}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{q}+\\var{n*l}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{l*m-p}w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{q+n*l}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{l*m-p}w}{\\var{l*m-p}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{q+n*l}}{\\var{l*m-p}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$w$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{q+n*l}/{l*m-p}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{q+n*l}/{l*m-p}", "maxValue": "{q+n*l}/{l*m-p}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}=\\var{g}$, &nbsp;$y=$&nbsp;[[0]].</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}=\\var{g}$, we can multiply both sides by $(y-\\var{f})$ to get rid of the fraction, get all the $y\\text{'s}$ on one side and the numbers on the other side, and then divide both sides by the coefficient of $y$ to get $y$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{d}y}{y-\\var{f}}}\\times(y-\\var{f})$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}\\times (y-\\var{f})$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}y+\\var{-g*f}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{d}y+\\var{-g}y$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{g}y+\\var{-g*f}+\\var{-g}y$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{d-g}y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{-g*f}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{d-g}y}{\\var{d-g}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{-g*f}}{\\var{d-g}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;$y$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{-g*f}/{d-g}}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{-g*f}/{d-g}", "maxValue": "{-g*f}/{d-g}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve&nbsp;$\\displaystyle{\\frac{z+\\var{h}}{z+\\var{j}}}=\\var{k}$ for $z$.</p>\n<p>$z=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\displaystyle{\\frac{z+\\var{h}}{z+\\var{j}}}=\\var{k}$, we can multiply both sides by $(z+\\var{j})$ to get rid of the fraction, get all the $z\\text{'s}$ on one side and the numbers on the other side, and then divide both sides by the coefficient of $z$ to get $z$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z+\\var{h}}{z+\\var{j}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}$&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{z+\\var{h}}{z+\\var{j}}}\\times(z+\\var{j})$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}\\times (z+\\var{j})$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z+\\var{h}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}z+\\var{k*j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z+\\var{h}-\\var{k}z$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k}z+\\var{k*j}-\\var{k}z$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{1-k}z+\\var{h}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k*j}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{1-k}z+\\var{h}-\\var{h}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k*j}-\\var{h}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;$\\var{1-k}z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{k*j-h}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td>&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{\\var{1-k}z}{\\var{1-k}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\frac{\\var{k*j-h}}{\\var{1-k}}}$</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$z$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{({k*j-h})/({1-k})}}$</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{k*j-h}/{1-k}", "maxValue": "{k*j-h}/{1-k}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}, {"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Solve $\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}=\\var{right}}$.</p>\n<p>$x=$&nbsp;[[0]]</p>", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>Given $\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}=\\var{right}}$, we can multiply both sides by $\\var{denom1}$ and by $\\var{denom2}$ to get rid of the fractions, get all the $x\\text{'s}$ on one side and the numbers on the other side, and then divide both sides by the coefficient of $x$ to get $x$ by itself.</p>\n<p></p>\n<table>\n<tbody>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\frac{x+\\var{add}}{\\var{denom1}}+\\frac{x}{\\var{denom2}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{right}$&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\left(\\frac{x+\\var{add}}{\\var{denom1}}\\right)\\times\\var{denom1}+\\left(\\frac{x}{\\var{denom2}}\\right)\\times\\var{denom1}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{right}\\times \\var{denom1}$</td>\n<td style=\"text-align: left;\">(multiply all terms by $\\var{denom1}$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;</td>\n<td></td>\n<td style=\"text-align: left;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{x+\\var{add}+\\frac{\\var{denom1}x}{\\var{denom2}}}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r1}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{(x+\\var{add})\\times\\var{denom2}+\\left(\\frac{\\var{denom1}x}{\\var{denom2}}\\right)\\times\\var{denom2}}$&nbsp;</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r1}\\times\\var{denom2}$</td>\n<td style=\"text-align: left;\">(multiply all terms by $\\var{denom2}$)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\displaystyle{\\var{denom2}x+\\var{a2}+\\var{denom1}x}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r12}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{sumdeno}x+\\var{a2}$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r12}$</td>\n<td style=\"text-align: left;\">(collect like terms)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">&nbsp;$\\var{sumdeno}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{r12}-\\var{a2}$</td>\n<td style=\"text-align: left;\">(collect like terms)</td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td>&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$\\var{sumdeno}x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\var{top}$</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\"></td>\n<td></td>\n<td style=\"text-align: left;\">&nbsp;</td>\n<td style=\"text-align: left;\"></td>\n</tr>\n<tr>\n<td style=\"text-align: right;\">$x$</td>\n<td>$=$</td>\n<td style=\"text-align: left;\">$\\displaystyle{\\simplify{{top}/({sumdeno})}}$</td>\n<td style=\"text-align: left;\">(divide by the coefficient of $x$)</td>\n</tr>\n</tbody>\n</table>"}], "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "{top}/{sumdeno}", "maxValue": "{top}/{sumdeno}", "correctAnswerFraction": true, "allowFractions": true, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}], "resources": []}]}], "contributors": [{"name": "Ben Brawn", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/605/"}]}