Solve an equation with a reciprocal

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Thomas Waters 5 years, 7 months ago

Created this as a copy of W2a: Solve an equation with a reciprocal-1.

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	3
c	integer	-6
b	integer	-9
d	number	9
s2	integer	-1
s1	integer	-1
b1	integer	-9
t	integer	7
an2	number	45
an1	number	142

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Value

xxxxxxxxxx
 
random(2..9)

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Description

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Generated value: `integer`

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1. Gap Mathematical expression
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Gap-fill

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

$x=\;$ 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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Taxonomy: mathcentre

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Thomas Waters 5 years, 7 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

History

Comment

Checkpoint description

Thomas Waters 5 years, 7 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`