How to write down all the integer values that satisfy an inequality.

Sometimes you will asked to write down all the integer values that satisfy an inequality. An integer can be a positive or negative whole number.

Example 1

Write down all the integer values that satisfy this inequality -3 < x < 4

Reading this inequality from left to right is says “-3 is less than x which is less than 4”.

This means that you need all the whole numbers that are between -3 and 4.

Start with the lowest whole number that satisfies the inequality then work your way up.

-2 is the lowest because “-3 is less than -2 which is less than 4”

Then you need -1 because “-3 is less than -1 which is less than 4”

Then you need 0 because “-3 is less than 0 which is less than 4”

Then you need 1 because “-3 is less than 1 which is less than 4”

Then you need 2 because “-3 is less than 2 which is less than 4”

Then you need 3 because “-3 is less than 3 which is less than 4”

So all the integer values you need are -2,-1,0,1,2 and 3.

Example 2

Write down all the integer values that satisfy this inequality -3 ≤ x < 1

Reading this inequality from left to right is says “-3 is less than or equal to x which is less than 1”.

This means that you need all the whole numbers that are between -3 and 1 but include -3 as x can be equal to it.

Start with the lowest whole number that satisfies the inequality then work your way up:

-3 is the lowest because “-3 is less than or equal to -3 which is less than 1”

Then you need -2 because “-3 is less than or equal to -2 which is less than 1”.

Then you need -1 because “-3 is less than or equal to -1 which is less than 1”

Then you need 0 because “-3 is less than or equal to 0 which is less than 1”

So all the integer values you need are -3,-2,-1 and 0.

Example 3

Write down all the integer values that satisfy this inequality -5 < x ≤ -1

Reading this inequality from left to right is says “-5 is less than x which is less than or equal to -1”.

This means that you need all the whole numbers that are between -5 and -1 but include -1 as x can be equal to it.

Start with the lowest whole number that satisfies the inequality then work your way up:

-4 is the lowest because “-5 is less than -4 which is less than or equal to -1”.

Then you need -3 because “-5 is less than -3 which is less than or equal to -1”.

Then you need -2 because “-5 is less than -2 which is less than or equal to -1”.

Then you need -1 because “-5 is less than -1 which is less than or equal to -1”.

So all the integer values you need are -4, -3, -2 and -1.

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