Equations: Linear equations 1a - rational answers

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Ruth Hand

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Ready to use

4 years, 2 months ago

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Christian Lawson-Perfect 2 years, 7 months ago

Published this.

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Ruth Hand 4 years, 2 months ago

Gave some feedback: Ready to use

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Ruth Hand 4 years, 2 months ago

Created this as a copy of Equations: Linear equations 1.

Name	Status	Author	Last Modified
Equations: Linear equations 1	Ready to use	Ruth Hand	17/04/2024 10:35
Equations: Linear equations 1a - rational answers	Ready to use	Ruth Hand	17/04/2024 10:52

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Question statement

Solve the following equations to find $x$ :

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	-9
b	integer	12
c	integer	-14
d	integer	9
f	integer	-7
g	integer	18
h	integer	-12
m	integer	-10
n	integer	-3
add	string	subtract
addsym	string	-
add2	string	add
add2sym	string	+
add3	string	subtract
add3sym	string	-
a1	rational	26/9
a2	rational	-209/9
a3	rational	69/56
a4	rational	-7/2
a5	rational	-67/72

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-20..20 except 0 except 1 except -1)

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: `integer`

-9

→ Used by:

Advice
"Part a)" - prompt

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Mathematical expression
  Add
Part c) Gap-fill
1. Gap Mathematical expression
  Add

Gap-fill

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

$\simplify{{a}x+{b} = {c}}$

$x=$ Unnamed gap

Advice

part a)

$\simplify{{a}x+{b} = {c}}$

The first step is to isolate all the $x$ -terms to one side of the equation.

To do that we will {add} $\var{abs(b)}$ onto both sides:

$\var{a}x = \simplify{{c-b}}$

Now we need to divide both sides by the coefficient of $x$ , to leave just one $x$ .

Dividing both sides by $\var{a}$ ,

$x = {\simplify{({c}-{b})/{a}}}$

part b)

$\frac{\simplify{{d}x + {f}}}{\var{g}} = \var{h}$

The first step is to rearrange by removing the fraction on the left. To do this we mulitply both sides by

$\var{g}$ .

$\begin{split} \frac{\simplify{{d}x + {f}}}{\var{g}} \times \var{g} &= \var{h} \times \var{g} \\\\ \simplify{{d}x + {f}} &= \var{h*g} \end{split}$

Next we isolate all the

$x$ -terms onto one side of the equation.

To do that we will {add2}

$\var{abs(f)}$ on both sides:

$\begin{split} \var{d}x &= \simplify[]{{h*g}-{f}} \\ &= \simplify[]{{h*g-f}} \end{split}$

Finally we need to divide both sides by the coefficient of

$x$ , to leave just one

$x$ .

Dividing both sides by $\var{d}$ ,

$x = \simplify[fractionNumbers]{{(h*g-f)/d}}$

part c)

$\simplify{{b}({c}x+{g})} = \var{d}$

Even though this looks different, this is quite similar to part b). We just have a multiplication rather than a division to deal with as the first step.

Rearrange to remove the multiplication on the left. To do this we divide both sides by $\var{b}$ :

$\begin{split} \frac{\simplify{{b}({c}x+{g})}}{ \var{b}} &= \frac{\var{d}}{\var{b}} \\ \\ \simplify{{c}x+{g}} &= \simplify[fractionNumbers]{{d/b}} \end{split}$

Next we isolate all the

$x$ -terms onto one side of the equation.

To do that we will {add3}

$\var{abs(g)}$ on both sides:

$\begin {split} \simplify{{c}x + {g}} \var{add3sym} \var{abs(g)} &= \simplify[fractionNumbers]{{d/b}} \var{add3sym} \var{abs(g)} \\ \var{c}x &= \simplify[fractionNumbers]{{d/b-g}} \end{split}$

Finally we need to divide both sides by the coefficient of

$x$ , to leave just one

$x$

Dividing both sides by $\var{c}$ :

$x = \simplify[fractionNumbers]{{(d/b-g)/c}}$

Give a worked solution to the whole question.

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Equations: Linear equations 1a - rational answers

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 4 years, 2 months ago

Ruth Hand 4 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: `integer`

Parts

Gap-fill

part a)

part b)

part c)

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Error

Equations: Linear equations 1a - rational answers

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 7 months ago

Ruth Hand 4 years, 2 months ago

Ruth Hand 4 years, 2 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

part a)

part b)

part c)

Generated value: `integer`