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How to Express Intervals As Inequalities

In mathematics, an interval is a range of numbers like the example "from 10 to 20." Intervals may be open, closed or semi-open. A closed interval includes the points at the limit (in the example, 10 and 20). An open interval does not include them (in the example, more than 10 and less than 20). A semi-open interval includes one limit point, but not the other. An inequality, on the other hand, is a statement of one of the following forms: x < a, x <= a, x > a or x >= a, where a is a constant. You can express intervals as inequalities.

Instructions

- 1
  Determine if your interval is open, closed or semi-open. If it is semi-open, determine which side is open and which is closed. For example, "more than 10 and less than or equal to 20" is semi-open (closed on the upper end).
- 2
  Find the lower limit of the interval; call this L. If the interval is closed, or semi-open and closed on the lower end, write L <= x. Otherwise, write L < x. In the example, write 10 < x.
- 3
  Find the upper limit of the interval; call this U. If the interval is closed, or semi-open and closed on the upper end, write x <= U. Otherwise, write x < U. In the example, write x <= 20.
- 4
  Join the two statements by writing them next to each other but with only one x. In the example 10 < x <= 20.

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