Equations: Linear equations 2 - unknowns on both sides

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Ruth Hand

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samira Al-Moustafa 4 months, 3 weeks ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 2 years, 6 months ago

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Ruth Hand 2 years, 7 months ago

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Ruth Hand 3 years, 6 months ago

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Created this as a copy of Solving linear equations: collecting like terms and solving.

Name	Status	Author	Last Modified
Solving linear equations: collecting like terms and solving	Ready to use	sean hunte	10/05/2019 02:18
Equations: Linear equations 2 - unknowns on both sides	Ready to use	Ruth Hand	27/10/2024 10:31
AC1 Solve linear equations	Ready to use	Megan Oliver	09/04/2024 15:10
AC2 Solve Linear equations with fractions 1	Ready to use	Andrew Neate	08/05/2024 13:14
AC7 Solve Linear equations with fractions 2	Ready to use	Will Morgan	08/05/2024 12:36

There are 28 other versions that do you not have access to.

Question statement

Give any introductory information the student needs.

			Name	Type	Generated Value

primes	list	[ 3, 5, 7, 11, 2 ]
denom1	integer	3
denom2	integer	5
add	integer	7
right	integer	-1
eans	rational	-25/4
r1	integer	-3
a2	integer	35
r12	integer	-15
top	integer	-50
sumdeno	integer	8

			Name	Type	Generated Value

a	integer	3
b	integer	6
c	integer	8
ans1	rational	6/5
d	integer	5
f	integer	5
g	integer	-7
ans2	rational	0
h	integer	4
j	integer	10
k	integer	10
ans3	integer	80
l	integer	2
m	integer	12
n	integer	11
p	integer	1
q	integer	3
ans4	rational	134
ansA	rational	25/23
ansB	rational	35/12
ansC	rational	-32/3
ansD	rational	-25/4

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
shuffle([2,3,5,7,11])

JME function reference

Description

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

Can an exam override the value of this variable?

Generated value: `list`

[ 3, 5, 7, 11, 2 ]

→ Used by:

add
denom1
denom2

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Number entry
  Add
Part b) Gap-fill
1. Gap Number entry
  Add
Part c) Gap-fill
1. Gap Number entry
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Gap-fill

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

Solve $\simplify{{l}({m}w-{n}) = {p}w+{q}}$

$w=$ Unnamed gap

Advice

Part a)

Given $\simplify{{l}({m}w-{n}) = {p}w+{q}}$ , we can expand the brackets, get all the $w$ 's on the left hand side and all the numbers on the right hand side, and then divide both sides by the coefficient of $w$ to get $w$ by itself.

$\simplify{{l}({m}w-{n})}$	$=$	$\simplify{{p}w+{q}}$

$\simplify{{lm}w+{nl}}$	$=$	$\simplify{{p}w+{q}}$

$\simplify[!cancelTerms,unitFactor]{{lm}w-{nl}-{p}w}$	$=$	$\simplify[!cancelTerms,unitFactor]{{p}w+{q}-{p}w}$

$\simplify{{lm-p}w-{nl}}$	$=$	$\var{q}$

$\var{lm-p}w-\var{nl}+\var{n*l}$	$=$	$\var{q}+\var{n*l}$

$\var{l*m-p}w$	$=$	$\var{q+n*l}$

$\displaystyle{\frac{\var{lm-p}w}{\var{lm-p}}}$	$=$	$\displaystyle{\frac{\var{q+nl}}{\var{lm-p}}}$

$w$	$=$	$\displaystyle{\simplify{{q+nl}/{lm-p}}} = \var{precround(ansA,1)} \text{ to 1 dp}$

Part b)

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 $y$ '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.

$\displaystyle{\frac{\var{d}y}{y-\var{f}}}$	$=$	$\var{g}$

$\displaystyle{\frac{\var{d}y}{y-\var{f}}}\times(y-\var{f})$	$=$	$\var{g}\times (y-\var{f})$

$\var{d}y$	$=$	$\simplify[unitFactor]{{g}y+{-g*f}}$

$\simplify[!cancelTerms,unitFactor]{{d}y+{-g}y}$	$=$	$\simplify[!cancelTerms,unitFactor]{{g}y+{-g*f}+{-g}y}$

$\var{d-g}y$	$=$	$\var{-g*f}$

$\displaystyle{\frac{\var{d-g}y}{\var{d-g}}}$	$=$	$\displaystyle{\frac{\var{-g*f}}{\var{d-g}}}$

$y$	$=$	$\displaystyle{\simplify{{-g*f}/{d-g}}}= \var{precround(ansB,1)}\text{ to 1 dp}$

part c)

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 $x$ '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.

$\displaystyle{\frac{x+\var{add}}{\var{denom1}}+\frac{x}{\var{denom2}}}$	$=$	$\var{right}$

$\displaystyle{\left(\frac{x+\var{add}}{\var{denom1}}\right)\times\var{denom1}+\left(\frac{x}{\var{denom2}}\right)\times\var{denom1}}$	$=$	$\var{right}\times \var{denom1}$	(multiply all terms by $\var{denom1}$ )

$\displaystyle{x+\var{add}+\frac{\var{denom1}x}{\var{denom2}}}$	$=$	$\var{r1}$

$\displaystyle{(x+\var{add})\times\var{denom2}+\left(\frac{\var{denom1}x}{\var{denom2}}\right)\times\var{denom2}}$	$=$	$\var{r1}\times\var{denom2}$	(multiply all terms by $\var{denom2}$ )

$\displaystyle{\var{denom2}x+\var{a2}+\var{denom1}x}$	$=$	$\var{r12}$

$\var{sumdeno}x+\var{a2}$	$=$	$\var{r12}$	(collect like terms)

$\var{sumdeno}x$	$=$	$\var{r12}-\var{a2}$	(collect like terms)

$\var{sumdeno}x$	$=$	$\var{top}$

$x$	$=$	$\displaystyle{\simplify{{top}/({sumdeno})}}= \var{precround(ansD,1)} \text{ to 1 dp}$	(divide by the coefficient of $x$ )

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Equations: Linear equations 2 - unknowns on both sides

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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samira Al-Moustafa 4 months, 3 weeks ago

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 3 years, 6 months ago

Ruth Hand 3 years, 6 months ago

Error in variable testing condition

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Generated value: `list`

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Gap-fill

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Error

Equations: Linear equations 2 - unknowns on both sides

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

samira Al-Moustafa 4 months, 3 weeks ago

Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 2 years, 7 months ago

Ruth Hand 3 years, 6 months ago

Ruth Hand 3 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

Generated value: `list`