// Numbas version: exam_results_page_options {"name": "Solve an equation with a reciprocal", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"stepsPenalty": 1, "scripts": {}, "gaps": [{"answer": "{an1}/{an2}", "showCorrectAnswer": true, "vsetrange": [0, 1], "scripts": {}, "checkvariablenames": false, "expectedvariablenames": [], "notallowed": {"message": "

Input as a fraction or an integer, not as a decimal.

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\\[\\simplify{{t} / ({a} * x + {b}) + {c} = {d}}\\]

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$x=\\;$ [[0]]

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If you want help in solving the equation, click on \"Show steps\". If you do so then you will lose 1 mark.

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Input all numbers as fractions or integers and not as decimals.

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Rearrange the equation by adding {-c} to both sides to get:
\\[\\simplify[std]{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]

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This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)

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and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.

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Solve this equation for $x$.

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Solve the following equation for $x$.

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Input your answer as a fraction or an integer as appropriate and not as a decimal.

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5/08/2012:

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Checked calculation.OK.

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Improved display in content areas.

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Solve for $x$: $\\displaystyle \\frac{a} {bx+c} + d= s$

"}, "functions": {}, "advice": "

Rearrange the equation by adding {-c} to both sides to get:
\\[\\simplify{{t} / ({a} * x + {b}) = {d} + { -c} = {d -c}}\\]
This gives \\[\\simplify{({a} * x + {b}) / {t} = 1 / {d -c}}\\] (this is because if $\\displaystyle \\frac{a}{b}=c$ then $\\displaystyle \\frac{b}{a}=\\frac{1}{c}$ on turning the fraction round the other way)
and so \\[\\simplify{({a} * x + {b}) = {t} / {d -c}}\\] on multiplying both sides by {t}.
Hence \\[\\simplify{{a} * x = {t} / {d -c} -{b} = ({a * an1} / {an2})}\\]
and so \\[\\simplify{x={an1}/{an2}}\\] is the solution on dividing both sides by {a}.

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