# Integer solutions to inequalities

When solving inequalities there will be a range of answers. Because any numbers represented by the range are acceptable, there are an amount of solutions to inequalities.

For example, if , then any number that is bigger than 3 is a possible answer, from any decimal slightly bigger than 3 to infinity.

Sometimes, only solutions are required.

### Example

List the integer solutions to .

This can be read as -5 is less than , which is less than 1.

That means that is larger than -5, but not equal to -5, so the smallest integer that can be is -4.

is less than 1, but not equal to 1, so the largest integer that can be is 0.

can also be the integers between -4 and 0.

This means that the integer solutions to are: -4, -3, -2, -1, 0.

Question

List the integer solutions of .

The in the centre of the inequalities has been multiplied by 2 to give . To find the solutions for , use inverse operations and divide all by 2.

is larger than -1.5, so the smallest integer solution is -1. is less than or equal to 4, so the largest integer solution is 4. can also be any number between these two solutions.

The integer solutions of are: -1, 0, 1, 2, 3, 4.