Solving linear inequalities

Error

There was an error loading the page.

Contributors

Adrian Jannetta

Feedback

From users who are members of Foundation Maths :

Adrian Jannetta

said

Should not be used

1 year, 7 months ago

History

○

Adrian Jannetta 1 year, 7 months ago

Gave some feedback: Should not be used

○

Adrian Jannetta 7 years, 6 months ago

Created this as a copy of Solving linear inequalities.

Name	Status	Author	Last Modified
Solving linear inequalities	Ready to use	Bradley Bush	20/11/2019 14:42
Solve quadratic inequalities	Ready to use	Bradley Bush	20/11/2019 14:42
Solving linear inequalities	Should not be used	Adrian Jannetta	31/08/2023 17:00
Ida's copy of Solve quadratic inequalities	draft	Ida Landgärds	13/04/2018 09:16
Ida's copy of Solving linear inequalities	draft	Ida Landgärds	13/04/2018 09:16
Solving linear inequalities [L5 Randomised]	Needs to be tested	Matthew James Sykes	25/07/2018 10:51
cormac's copy of Solving linear inequalities	draft	cormac breen	24/10/2018 13:44
cormac's copy of Solve quadratic inequalities	draft	cormac breen	24/10/2018 13:46
Solving linear inequalities	draft	Xiaodan Leng	11/07/2019 01:43

There are 66 other versions that do you not have access to.

Question statement

Solve the following linear inequalities by finding the set of possible values for $x$ . State your answers as fractions where applicable.

Give any introductory information the student needs.

			Name	Type	Generated Value

a	list	List of 10 items
b	list	List of 10 items
c	integer	3
x		Definition of variable `x` is empty.

Automatically regenerate variables?

Name

Data type

Value

xxxxxxxxxx
 
repeat(random(2..10),10)

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`

[ 6, 9, 8, 3, 10, 10, 6, 3, 10, 8 ]

This variable doesn't seem to be used anywhere.

Parts

Part a) Gap-fill
1. Gap Mathematical expression
  Add
Part b) Gap-fill
1. Gap Gap 0. Mathematical expression
  Add
2. Gap Gap 1. Choose one from a list
  Add

Gap-fill

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

$\simplify{{a[2]}x<{a[3]}}$

$x<$ Unnamed gap

Advice

As with regular linear equations, we aim to isolate the variable by subtracting any constants when dividing by the $x$ coefficient. The only major difference is that when we divide or multiply by a negative number, the inequality sign is reversed.

For example, the following inequality is true:

$-3 \lt -2$

When we multiply both sides by $-2$ , the inequality sign must reverse:

$6 \gt 4$

a)

To put $x$ on its own, we need to add $\var{a[0]}$ to both sides of the inequality.

$\begin{align} \simplify{x-{a[0]}}&<\var{a[1]}\\[1em] \var{x}&<\simplify[]{{a[1]}+{a[0]}}\\[1em] x&<\simplify{({a[1]}+{a[0]})}\text{.} \end{align}$

b)

In this example we find $x$ by dividing both sides by the coefficient of $x$ , $\var{a[2]}$ .

$\begin{align} \simplify{{a[2]}}x&<\var{a[3]}\\[1em] x&<\simplify{{a[3]}/{a[2]}}\text{.} \end{align}$

c)

$\begin{align} \simplify{{a[6]}x-{a[4]}}&<\var{a[5]}\\[1em] \var{a[6]}x&<\var{a[5]}+\var{a[4]} & \text{Add } 8 \text{ to get } x \text{ on its own.}\\[1em] x&<\simplify[]{({a[5]}+{a[4]})/{a[6]}} & \text{ Divide by } \var{a[6]} \text{.} \\[1em] x&<\simplify{({a[5]}+{a[4]})/{a[6]}}\text{.} \end{align}$

d)

In this example, take the constants to one side, and keep the $x$ term on the other. Divide through by the negative $x$ -coefficient to find an inequality for $x$ . Notice that where you divide (or multiply) an equality by a negative value, the inequality sign is reversed.

$\begin{align} \simplify{{-a[6]}x - {a[4]}} &< \var{a[5]} \\[1em] \var{-a[6]}x &< \var{a[5]} + \var{a[4]} & \text{Add } \var{a[4]} \text{ to both sides.} \\[1em] x &> \simplify[]{({a[5]}+{a[4]})/-{a[6]}} \text{ Divide by } \var{-a[6]} \text{. The inequality is reversed.} \\[1em] x &> \simplify{({a[5]}+{a[4]})/-{a[6]}}\text{.}\\ \end{align}$

e)

In this example, separate the constants and the $x$ -term, then divide by the $x$ -coefficient to find an inequality for $x$ .

$\begin{align} \simplify{{b[0]}x-{b[1]}}&<\simplify{{b[3]}-{b[2]}x}\\[1em] \simplify{({b[0]}+{b[2]})x}&<\simplify{{b[3]}+{b[1]}}\\[1em] x&<\simplify{({b[3]}+{b[1]})/({b[0]}+{b[2]})}\text{.}\\[1em] \end{align}$

f)

In this example, separate the $x$ -term from all other terms and remember to reverse the inequality when dividing by $\simplify{{a[7]}-{b[4]}}$ .

$\begin{align} \simplify{-{b[4]}x+{a[8]}a}&>\simplify{{b[5]}+b-{a[7]}x}\\[1em] \simplify{{a[7]}-{b[4]}}x&>\simplify{{b[5]}+b-{a[8]}a}\\[1em] x&<\simplify{(-{b[5]}-b+{a[8]}a)/({b[4]}-{a[7]})}\text{.}\\[1em] \end{align}$

In this example, a simple way to solve for $x$ is to divide by $-\var{c}$ before rearranging the rest of the equation by subtracting $g$ from both sides.

$\begin{align} \simplify{-{c}(x+g)}&>\simplify{6h-{c}{a[0]}}\\[1em] \simplify{(x+g)}&<\simplify[]{6h/-{c}+{a[0]}}\\[1em] x&<\simplify[]{6h/-{c}+{a[0]}-g}\\[1em] x&<\simplify{{a[0]}-6h/{c}-g}\text{.} \end{align}$

Give a worked solution to the whole question.

Use this tab to check that this question works as expected.

There was an error which means the tests can't run:

Part	Test	Passed?
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Gap-fill
Gap-fill		Hasn't run yet
Mathematical expression
Mathematical expression		Hasn't run yet
Choose one from a list
Choose one from a list		Hasn't run yet

This question is used in the following exam:

Bridging Course Tutorial 1 by Daniel Mansfield in Fundamentals of Mathematics.

Loading...

Error

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adrian Jannetta 1 year, 7 months ago

Adrian Jannetta 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: `list`

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

Loading...

Error

Solving linear inequalities

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Adrian Jannetta 1 year, 7 months ago

Adrian Jannetta 7 years, 6 months ago

Error in variable testing condition

Error

Warning

Generated value: list

Parts

Gap-fill

a)

b)

c)

d)

e)

f)

Generated value: `list`