Solving equations. (Video)

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Bill Foster

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Bill Foster 12 years, 3 months ago

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Question statement

Solve the following linear equation for $x$ .

Give any introductory information the student needs.

			Name	Type	Generated Value

a	integer	10
c	integer	11
b	integer	10
d	integer	2
g	integer	2
f	integer	1
s3	integer	1
s2	integer	1
s1	integer	-1
td	integer	2
tc	integer	11

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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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Advice
"Unnamed part" - prompt
"Unnamed part" → "Unnamed gap" - Correct answer

Parts

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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.

$\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}$
Input your answer as a fraction or an integer. Do NOT input the answer as a decimal.

$x =$ Unnamed gap

Click on Show steps to see a video of a solution of a similar problem.

Advice

Given the equation

$\simplify[std]{{a} * x + {b} = {f}/{g}({c} * x + {d})}$ we first multiply both sides by

$\var{g}$ to get

$\simplify[std]{{g}*({a} * x + {b} )= {f}*({c} * x + {d})}.$

Then expand both sides of this equation to get:

$\simplify[std]{{g*a} x + {g*b} = {f*c}x + {f*d}}.$

and then collect together all the constant terms on the right hand-side, and collect together all the terms in $x$ on the left-hand side of the equation.

The equation can then be written as:

$\simplify[std]{({g*a}-{f*c})x=({f*d}+{-g*b})}$ i.e.

$\simplify{{g*a-f*c}x={f*d-b*g}}$
which gives

$x =\simplify[std]{{(f*d-b*g)}/{(g*a-f*c)}}$ as the solution.

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Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

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Checkpoint description

Bill Foster 12 years, 3 months ago

Error in variable testing condition

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Warning

Generated value: `integer`

Parts

Gap-fill

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Solving equations. (Video)

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

History

Comment

Checkpoint description

Bill Foster 12 years, 3 months ago

Error in variable testing condition

Error

Warning

Generated value: integer

Parts

Gap-fill

Generated value: `integer`