Inequalities on a Number Line

An inequality is when you have a relationship between two values of expressions which are not equal to each other.

There are a few different options for different types of inequalities:

• Greater than (>) where one expression or value is greater than another, e.g. 7 > 5
• Less than (<) where one expression or value is less than another, e.g. 9 < 2 x 6
• Greater than or equal to (≥) where one expression or value is greater than or equal to another, e.g. 20 + 4 ≥ 17
• Less than or equal to (≤) where one expression or value is less than or equal to another, e.g. 18 ≤ 9 x 2
• Not equal to (≠) where one expression or value is not equal to another

To show an inequality on a number line with just one value, follow these steps:

• find the value that you are going to need.
• represent the value with either an open or closed circle (see below)
• draw a line from the circle to the left end of the number line if the symbol is < or ≤
• draw a line from the circle to the right end of the number line if the symbol is > or ≥
• put an arrow at the end of the number line to represent continuation past the end of the number line

To show an inequality on a number line between two values, follow these steps:

• find the values that you are going to need.
• represent the values with either an open or closed circle (see below)
• draw a line joining the two circles

When we are looking at inequalities on a number line, we use open and closed circles to represent the values:

• for greater than (>) and less than (<) we use open circles to show that the value itself is not included.
• for greater than or equal to (≥) and less than or equal to (≤) we use closed circles to show that the value itself is included.

Here are some examples of inequalities on a number line.

Example 1) Represent x > 7 on the number line.

Step 1) Identify the value on the number line.

The value needs to be an open circle as the symbol is >

Step 2) Draw line from the value to the end of the line.

The line needs to go to the right as the symbol is > an arrow goes at the end of the line

Example 2) Represent y ≤ 3 on the number line.

Step 1) Identify the value on the number line.

The value needs to be a closed circle as the symbol is ≤

Step 2) Draw line from the value to the end of the line.

The line needs to go to the left as the symbol is ≤ an arrow goes at the end of the line.

Example 3) Represent 6 < x < 10 on the number line.

Step 1) Identify the values on the number line.

The values both need to be open circles as the symbols are both <

Step 2) Draw line from one circle to the other.

Example 4) Represent -3 < x ≤ 2 on the number line.

Step 1) Identify the values on the number line.

The value -3 needs to be an open circle as the symbol is <.

The value 2 needs to be a closed circle as the symbol is ≤

Step 2) Draw line from one circle to the other.

Example 5) Represent -5 ≤ x < 3 on the number line.

Step 1) Identify the values on the number line.

The value -5 needs to be a closed circle as the symbol is ≤.

The value 3 needs to be an open circle as the symbol is <

Step 2) Draw line from one circle to the other.

Example 6) Represent the inequalities x ≤ -1 ½ or x ≥ ½ on the number line.

These two inequalities are different from the previous ones as there is are no common values which matches both of them. In effect these inequalities are showing what values of x are not allowed.

Step 1) Identify the values on the number line.

The value -1 ½ needs to be a closed circle as the symbol is ≤.

The value ½ needs to be a closed circle as the symbol is ≥

Step 2) Draw line from each of the circles in the right direction.

• The line from -1 ½ needs to go to the left as the symbol is ≤ an arrow goes at the end of the line.
• The line from ½ needs to go to the right as the symbol is ≥ an arrow goes at the end of the line.

We have a range of different inequality worksheets with number lines.

We have split the sheets into two sections:

• number lines with positive numbers only
• number lines with both positive and negative numbers

Sheets 1 and 2 involve finding single inequalities with a single value on a number line.

Sheet 1 contains integer values; sheet 2 contains halves as well as integer values

Sheets 3 and 4 involve finding combined inequalities between two values.

Sheets 1 and 2 involve finding single inequalities with a single value on a number line.

Sheet 1 contains integer values; sheet 2 contains halves as well as integer values

Sheets 3 and 4 involve finding combined inequalities between two values.

This short video walkthrough shows several problems from our Inequalities on a Number Line Worksheet 3 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

Sheet 1 involves finding single inequalities.

Sheet 2 involves finding a range of inequalities.

This short video walkthrough shows several problems from our Spot the Inequality Worksheet 2 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, please check out the video below!

We also have a range of other worksheets and resources to help you understand how inequalities work.

Here is our selection of number lines from 0 to 1.

On this page you will find:

• 0 to 10 standard and decimal number lines
• standard 0 to 1 number lines in both portrait and landscape;
• fraction - decimal number lines from 0 to 1.
• fraction - decimal - percent number lines from 0 to 1
• number lines from 0 to 1 with fraction strips

Here is our selection of free printable negative number lines with only negative numbers.

Using these sheets will help your child to:

• see visually the order of negative numbers in a number line;
• learn how negative numbers are positioned on a number line.

Here is our selection of integer number lines.

Using these sheets will help your child to:

• learn their place value, and ordering of numbers;
• compare the position of two numbers visually on a number line.

Number lines include:

• 0 to 10
• 0 to 100
• 0 to 1000
• 0 to 10000

Here is our selection of decimal number lines.

Using these sheets will help your child to:

• learn their place value, and ordering of decimals;
• compare the position of two decimals visually on a number line.
• understand fraction-decimal equivalence using number lines from 0 to 1

These first grade math worksheets will give your child a good grasp of place value and number sequences up to 100.

Using these sheets will help your child to:

• count on and back by ones;
• position numbers to 100 on a number line.

The Math Salamanders hope you enjoy using these free printable Math worksheets and all our other Math games and resources.

We welcome any comments about our site or worksheets on the Facebook comments box at the bottom of every page.