Which Number Line Represents the Solution Set for the Inequality.
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In order to admission this I need to be confident with:
Ordering numbers including negatives and decimals
This topic is relevant for:
Inequalities On A Number Line
Here we will learn virtually inequalities on a number line including how to represent inequalities on a number line, translate inequalities from a number line and listing integer values from an inequality.
At that place are besides inequalities on a number line worksheets based on Edexcel, AQA and OCR exam questions, forth with further guidance on where to get next if you’re all the same stuck.
What are inequalities on a number line?
Inequalities on a number line
let the states to visualise the values that are represented by an inequality.
To stand for inequalities on a number line we show the range of numbers past drawing a straight line and indicating the finish points with either an open circle or a airtight circle.
An open up circle shows it
does not include
the value.
A closed circle shows it
does include
the value.
Due east.m.
The solution set of these numbers are all the existent numbers between
i
and
five
.
Equally
1
has an open circle, it
does not include ‘
ane
’
but does include anything higher, up to and
including
five
equally this end indicate is indicated with a closed circumvolve.
We can represent this using the inequality
1 < 10 \leq5
We can as well state the
integer
values (whole numbers) represented past an inequality.
In this case, the integers
2, three, 4
and
5
are all greater than
i
merely less than or equal to
5
.
The solution gear up can represent all the real numbers shown within the range and these values can besides be negative numbers.
What are inequalities on a number line?
How to represent inequalities on a number line
In social club to represent inequalities on a number line:
 Identify the value(s) that needs to be indicated on the number line.

Make up one’s mind if information technology needs an open circle or a closed circle;
< or > would need an open up circle
\leq
or
\geq
would demand a closed circle.  Indicate the solution set with a straight line to the left hand side or correct paw side of the number or with a directly line between the circles.
Eastward.g.
Represent
ten < 3
on a number line
An open up circle needs to exist indicated at ‘
iii
’ on the number line.
As
10 < three
is ‘
x
is less than
3
’, the values to the left hand side of the circumvolve need to be indicated with a line.
E.chiliad.
Represent
two<{x}\leq{6}
on a number line.
An open up circle needs to be indicated to a higher place ‘
2
’ and a closed circle needs to be indicated above ‘
halfdozen
’.
Then draw a line between the circles to indicate any value between these circles.
How to represent inequalities on a number line
Inequalities on a number line worksheet
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Related lessons on inequalities
Inequalities on a number line
is role of our series of lessons to support revision on
inequalities. You may find information technology helpful to starting time with the primary inequalities lesson for a summary of what to expect, or use the step past step guides below for further detail on private topics. Other lessons in this serial include:
 Inequalities
 Solving inequalities
 Quadratic inequalities
 Inequalities on a graph
Inequalities on a number line examples
Example i: unmarried values
Represent
x > 3
on a number line.
 Place the value that needs to exist on the number line.
In this example it is
3
.
2Decide if this needs to be indicated with an open circle or a closed circle.
Equally the symbol is > and then information technology will be an open up circle.
threeDecide if the straight line needs to be drawn to the right or the left of the circle.
As
10
is greater than
iii
the straight line needs to be fatigued to the correct hand side of the circle to show the solution prepare of values greater than
3
.
Instance 2: unmarried values
Represent
−2\geq{x}
on a number line.
Identify the value that needs to be on the number line.
In this example it is
−two
.
Decide if this needs to be indicated with an open up circle or a closed circle.
Every bit the symbol is
\geq
and then it will be a closed circle.
Make up one’s mind if the straight line needs to exist drawn to the correct or the left of the circle.
As
x
is less than or equal to
−2
the straight line needs to be drawn to the left hand side of the circle to show the solution set up of values less than
−ii
.
Example 3: values within a range
Stand for
ii\leq{x}\leq{7}
on a number line.
Identify the values that need to be indicated on the number line.
In this case they are
2
and
7
.
Decide if they demand to be indicated with open up circles or closed circles.
As the symbols are both at that place will exist two closed circles.
Draw a straight line between the circles to represent the solution set.
Example iv: values within a range
Represent
−2<{x}\leq{3}
on a number line.
Identify the values that demand to be indicated on the number line.
In this example they are
−ii
and
3
.
Make up one’s mind if they demand to be indicated with open circles or closed circles.
As the symbols are < and
\leq
there will exist an open circle and a closed circle.
Draw a straight line between the circles to represent the solution set.
Example five: writing an inequality from a number line
Write the inequality that is shown on this number line.
Identify the value indicated.
In this example it is ‘
4
’.
Decide which inequality symbol to use.
As the circle is closed and the values indicated are greater than
iv
nosotros employ the inequality is
x\geq{4}
Instance halfdozen: writing an inequality from a number line
Write the inequality that is shown on this number line:
Identify the values indicated on the number line.
In this example they are
−2
and
four
.
Decide which inequality symbol to use.
Every bit the circle above the
−2
closed we include the
−2
and use
ii\leq{x}.
As the circumvolve higher up the
4
is open nosotros do not include the
iv
and use
x < 4 .
Put the inequalities together.
Instance vii: listing integer values in a solution gear up
List the integer values satisfied past the inequality
four\leq{10}<two
Identify the values indicated on the number line.
In this example they are
−4
and
two
.
−4
is included as information technology is followed by
\leq
two
is not included every bit < is before it.
Example eight: listing integer values in a solution prepare from a number line
Listing the integer values satisfied by the inequality shown on the number line beneath.
Identify the values indicated on the number line.
In this case they are
2
and
4
.
−2
is non included as it is represented by an open circle.
4
is included as information technology is represented by a closed circle.
Common misconceptions

Wrong identification inequality symbols
A mutual mistake is to misfile open circles and airtight circles:
Open circles do not include the value so require a ‘<’ sign.
Closed circles practise include the value so require a
‘\leq’

Incorrect ordering of negative numbers
A common fault is to not recognise the symmetry about
‘0’
on the number line, and therefore not comparing the size of negative numbers correctly.
East.g.
v
is greater than one as they are ordered
1
,
2, 3, 4,
5
on a number line.
But
−5
is less than
−i
as they are ordered
−5
,
−iv, −iii, −2,
−i
,
0, i, 2, 3
on a number line.

Wrong estimation of the inequality symbol
The direction of the inequality sign shows if the solution set is ‘greater than’ or ‘less than’. This tin be confused when both sides of the inequality are switched. For example
ten > eight
is the same as
8 < x
and
‘10’
is greater than
8
every bit the inequality sign is open towards the
‘10’
.
 Not list all of the possible values in a solution set
Usually integer values are requested to exist listed in a solution set.
‘0’
tin sometimes be forgotten.
 Not because real numbers
In the inequality
ii\leq{10}<4
, the highest integer value that satisfies the inequality is
‘3’
. However, real numbers larger than
three
only less than
4
are as well satisfied by this inequality.
Practice inequalities on a number line questions
5
is non included in the solution set every bit it is ‘>’ so an open circle is needed. The inequality sign is open towards the
‘ten’
indicating it has values greater than
5
and so the line is drawn to the right hand side of the circumvolve.
7
is included in the solution set every bit it is
‘\leq’
then a airtight circle is needed. The inequality sign is airtight towards the
‘10’
indicating it has values less than
7
so the line is fatigued to the left hand side of the circle.
1
is not included in the solution gear up equally it is ‘<’ so an open up circumvolve is needed.
viii
is included in the solution set every bit it is ‘
\leq
‘ so a airtight circle is needed. A line is drawn between the circles to bespeak that all values in between are in the solution ready.
iii
and
4
are not included in the solution set every bit both signs are ‘<’ and then open up circles are needed. A line is drawn between the circles to indicate that all values in between are in the solution set.
6
is indicated with a closed circle then this value is included in the solution set. The pointer is drawn to the left hand side to indicate values less than
six
.
4
is indicated past an open circumvolve so this value is not included in the solution set therefore requires a ‘<’ symbol.
2
is indicated by a closed circumvolve so this value is included in the solution ready therefore requires a
‘\leq’
symbol. A line between the circles indicates all values in betwixt are in the solution set.
3, two, 1, 0, one, 2, three, 4
‘<’ follows
3
which means this value is not included in the solution set up.
‘\leq’
is before
iv
which means this value is included in the solution set up. All the integers greater than
3
and up to and including
4
are in the solution set.
Both inequality signs are ‘<’ which ways these values are not included in the solution set. All the integers greater than
4
and less than
one
are in the solution set.
1
is indicated with a closed circle so this value is included in the solution gear up.
4
is indicated with an open circle then this value is not included in the solution prepare. All of the integers greater than and including
ane
and up to
4
are included in the solution set.
Both
1
and
ii
are indicated with closed circles so these values are included in the solution set up. All of the integers greater than and including
ane
and up to and including
two
are included in the solution set.
Inequalities on a number line GCSE questions
1. John buys
x
bananas and
y
pears.
He buys
 At to the lowest degree
5
bananas  At near nigh
ix
pears  He buys more pears than bananas
1 of the inequalities for this data is
x\geq5
Write downwards two more than inequalities for this information
(2 marks)
Show respond
2.
(a) Show the inequality
x > 4
on this number line.
(b) Write downward the inequality for
x
that is shown on this number line
(three marks)
Testify respond
(a)
Open circle at
4
(1)
Arrow indicating values greater than
4
(i)
(b)
x\leq7
(1)
3.
(a) Write downwardly an inequality for
10
that is shown on this number line
(b)
(i) Testify the inequality
3\leq{ten}<2
on this number line.
(2) List the integers that are included in the solution set
(6 marks)
Show answer
(a)
2 < x
or
x\leq 7
(i)
2 < x \leq 7
(1)
(b)
Closed circle at
iii
or for open circle at
2
(1)
(1)
2, 1,
,
1
(1)
three, two, 1, 0, 1
(1)
Learning checklist
You have at present learned how to:
 Place inequalities from a number line
 Show inequalities on a number line
 List integer values in the solution set
Still stuck?
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Which Number Line Represents the Solution Set for the Inequality
Source: https://thirdspacelearning.com/gcsemaths/algebra/inequalitiesonanumberline/