Solving equations

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Bill Foster

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Bill Foster 55 years, 4 months ago

Created this.

Name	Status	Author	Last Modified
Solving equations	draft	Bill Foster	06/08/2020 08:42
Solving equations 2	draft	Lois Rollings	29/07/2016 13:43

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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	5
c	integer	-1
b	integer	1
d	number	3
s2	integer	-1
s1	integer	1
t	integer	6
an2	number	20
an1	number	2
b1	integer	1

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Name

Data type

Value

xxxxxxxxxx
 
random(2..9)

JME function reference

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

Gap-fill
1. Gap Mathematical expression
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1. Step Information only

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}.

Give a worked solution to the whole question.

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This question is used in the following exams:

Equations by Elena Stylianou in Elena's workspace.
Peter's copy of Equations by Peter Chleboun in Peter's workspace.
Bradford: Solving simple linear equations by Bill Foster in Bill's workspace.
Solving Linear Equations by Hayley Bishop in Hayley's workspace.
Maths Support: Solving linear equations by Christian Lawson-Perfect in Maths Support Wiki.
Jinhua's copy of Maths Support: Solving linear equations by Jinhua Mathias in Jinhua's workspace.
mathcentre: Solving simple linear equations by Bill Foster in Bill's workspace.
ACC1012 CBAs 1-3 by Man Isha Kaur in Man Isha's workspace.
Solving Linear Equations by Gareth Woods in Gareth's workspace.
Revision by Elena Stylianou in Elena's workspace.
Jack's copy of ACC1012 CBAs 1-3 by Jack Aiston in Jack's workspace.
mathcentre: Diagnostic test - Basic maths by Bill Foster in Bill's workspace.
Bradford: Diagnostic test - Basic maths by Bill Foster in Bill's workspace.
Basic Maths Revision by Gareth Woods in Gareth's workspace.
Extra Maths Checkup by Jamie Wood in Jamie's workspace.
Solving equations: 1 by Aneela Arshad in Aneela's workspace.
maths skills 1 by cormac murphy in cormac's workspace.
Combined ACC1012 v10 by Jack Aiston in Jack's workspace.
Combined ACC1012 v7 by Jack Aiston in Jack's workspace.
Combined ACC1012 V8 by Jack Aiston in Jack's workspace.
Combined ACC1012 v9 by Jack Aiston in Jack's workspace.

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Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

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Bill Foster 55 years, 4 months ago

Error in variable testing condition

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Generated value: `integer`

Parts

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Solving equations

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 55 years, 4 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`