Solve an equation with a reciprocal

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Bill Foster

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6 years, 4 months ago

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Bill Foster 6 years, 4 months ago

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Newcastle University Mathematics and Statistics 9 years, 2 months ago

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Name	Status	Author	Last Modified
Solve an equation with a reciprocal	Ready to use	Newcastle University Mathematics and Statistics	20/11/2019 14:50
Luis's copy of Solve an equation with a reciprocal	draft	Luis Hernandez	30/11/2018 00:44
W2a: Solve an equation with a reciprocal-1	Ready to use	Timur Zaripov	17/06/2022 09:37
Solve an equation with a reciprocal	draft	Thomas Waters	11/09/2019 21:47

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Question statement

Solve the following equation for $x$ .

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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	6
c	integer	-1
b	integer	-5
d	number	10
s2	integer	-1
s1	integer	-1
b1	integer	-5
t	integer	3
an2	number	66
an1	number	58

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Value

xxxxxxxxxx
 
random(2..9)

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Description

Describe what this variable represents, and list any assumptions made about its value.

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Generated value: `integer`

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Parts

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1. Gap Mathematical expression
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Gap-fill

Ask the student a question, and give any hints about how they should answer this part.

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

$x=\;$ Unnamed gap

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

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

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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Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

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Generated value: `integer`

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Solve an equation with a reciprocal

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Bill Foster 6 years, 4 months ago

Newcastle University Mathematics and Statistics 9 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`