# Which Number Line Represents the Solution Set for the Inequality

Which Number Line Represents the Solution Set for the Inequality.

## 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.

## How to represent inequalities on a number line

In social club to represent inequalities on a number line:

1. Identify the value(s) that needs to be indicated on the number line.
2. 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.
3. 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.

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 ‘
half-dozen
’.

Then draw a line between the circles to indicate any value between these circles.

## Inequalities on a number line examples

### Example i: unmarried values

Represent

x > 3

on a number line.

1. 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.

In this example it is

−two
.

Every bit the symbol is

\geq

and then it will be a closed 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.

In this case they are

2

and

7
.

As the symbols are both at that place will exist two closed circles.

### Example iv: values within a range

Represent

−2<{x}\leq{3}

on a number line.

In this example they are

−ii

and

3
.

As the symbols are < and

\leq

there will exist an open circle and a closed circle.

### Example five: writing an inequality from a number line

Write the inequality that is shown on this number line.

In this example it is ‘
4
’.

As the circle is closed and the values indicated are greater than

iv

nosotros employ the inequality is

x\geq{4}

### Instance half-dozen: writing an inequality from a number line

Write the inequality that is shown on this number line:

In this example they are

−2

and

four
.

### Instance vii: listing integer values in a solution gear up

List the integer values satisfied past the inequality

-four\leq{10}<two

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.

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.

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

x

bananas and

y

pears.

• 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)

(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

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## Which Number Line Represents the Solution Set for the Inequality

Source: https://thirdspacelearning.com/gcse-maths/algebra/inequalities-on-a-number-line/

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