Equations: Linear equations 1

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Ruth Hand

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4 years, 2 months ago

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Christian Lawson-Perfect 2 years, 6 months ago

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Ruth Hand 4 years, 2 months ago

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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

Give any introductory information the student needs.

			Name	Type	Generated Value

a	number	-19.1
b	number	3.8
c	number	-14.8
d	number	-0.2
f	number	-16.5
g	number	14.3
h	number	17.1
m	number	-15.4
n	number	-19
add	string	subtract
addsym	string	$-$
add2	string	add
add2sym	string	$+$
add3	string	subtract
add3sym	string	$-$
tofroma	string	from
tofromb	string	to
tofromc	string	subtract
a3	number	0.969772404

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
random(-20..20 #0.1 except 0)

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

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Generated value: `number`

-19.1

This variable doesn't seem to be used anywhere.

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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} $\var{abs(b)}$ {tofroma} both sides:

$\begin{split} \simplify{{a}x + {b}} = {{ \end{split}$

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

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

$\begin{split} x &= \frac{\simplify{{c}-{b}}}{\var{a}} \\ &=\simplify{{(c-b)/a}} \end{split}$

Rounding your answer as required,

$x = \var{precround((c-b)/a,2)}$

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 to one side of the equation.

To do that we will {add2}

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

$\begin{split} \simplify{{d}x + {f}} \var{add2sym} \var{abs(f)} &= \var{h*g} \var{add2sym} \var{abs(f)} \\ \var{d}x &= \simplify{{h*g}-{f}} \end{split}$

Finally we need to divide both sides by the coefficient of

$x$ , to leave just one

$x$ .

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

$\begin{split} x &= \frac{\simplify{{h*g}-{f}}}{\var{d}} \\ &= \var{(h*g-f)/d} \end{split}$

Rounding your answer as required,

$x = \var{precround((h*g-f)/d,2)}$

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 $\var{b}$ :

$\begin{split} \frac{\simplify{{b}({c}x+{g})}}{ \var{b}} &= \frac{\var{d}}{\var{b}} \\ \\ \simplify{{c}x+{g}} &= \var{precround(d/b,3)} \end{split}$

Do the division on the right with a calculator and round to 3 decimal places. Always use at least one more decimal place when rounding during the calculation than is required in your answer, to be on the safe side.

Next we isolate all the

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

To do that we will {add3}

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

$\begin {split} \simplify{{c}x + {g}} \var{add3sym} \var{abs(g)} &= \var{precround(d/b,3)} \var{add3sym} \var{abs(g)} \\ \var{c}x &= \var{precround(d/b - g,3)} \end{split}$

Finally we need to divide both sides by the coefficient of

$x$ , to leave just one

$x$

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

$\begin{split} x &= \frac{\var{precround(d/b - g,3)}}{\var{c}} \\ &= \var{(d/b-g)/c} \end{split}$

Rounding your answer as required,

$x = \var{precround((d/b - g)/c,2)}$

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Christian Lawson-Perfect 2 years, 6 months ago

Ruth Hand 4 years, 2 months ago

Ruth Hand 4 years, 2 months ago

Error in variable testing condition

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part a)

part b)

part c)

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Equations: Linear equations 1

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 2 years, 6 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: number

Parts

Number entry

Advanced settings

part a)

part b)

part c)

Generated value: `number`