# How to write down all the integers that satisfy an inequality between two numbers.

Updated on May 10, 2011

If you are asked to write down all the integers that satisfy the inequality -3 < x ≤ 4, then you are looking for all the values of x that are more -3 and less than or equal to 4.

This is because -3 < x means x > -3 (x is more than 3) and x ≤ 4 means x is less than or equal to 4.

Also an integer is a whole number so you don’t need to write down any decimals or fractions.

So the integers that satisfy -3 < x ≤ 4 are -2,-1, 0, 1, 2, 3 and 4.

Let’s take a look at another question:

Write down all the integers that satisfy the inequality -2 ≤ x < 3.

Here, -2 ≤ x means x ≥ -2 so you want all the integers more than or equal to -2.

Also x < 3 means all the integers less than 3.

So the required integers are -2,-1, 0, 1 and 2.

Let’s take a look at a harder example.

Write down all the integers that satisfy -6 ≤ 2x ≤ 5

This time you have 2x in the centre of the inequality, so the first thing to do is divide everything by 2.

This gives:

-3 ≤ x ≤ 2.5

Now -3 ≤ x is the same as x ≥ -3 so you need all the integers more than or equal to -3.

Also x ≤ 2.5 means you need all the integers less than or equal to 2.5 (don’t include 2.5 as 2.5 is a decimal and not an integer).

So the required integers are:

-3, -2, -1, 0, 1 and 2.

For some other maths help take a look at some of my other hubs:

Adding (or taking) two fractions together. Step by step fraction guide.

Working out percentages of amounts using a calculator method.

Stationary points. How to find a stationary point on a graph (turning points)

How to complete the square on a quadratic equation (completing the square).

Converting between millimetres and metres (metric units of length 1000mm = 1m)

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