When solving inequalities there will be a range of answers. Because any numbers represented by the range are acceptable, there are an infinite 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 integer solutions are required.
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.
List the integer solutions of .
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.