How to Represent Inequalities in One Variable

The inequality x > 3 means all numbers greater than 3. The set of numbers that makes the inequality true is called the solution set of the inequality. An instance of this numbers such as 4 is a solution to x > 3.

The graph of x > 3 is shown on the number line below. The “empty circle” means that the solution does not include 3. The highlighted part of the number line (blue ray) means that it includes all real numbers greater than 3 and the arrow indicates that it goes up to infinity.

representing inequalities

Another notation to represent x > 3 is (3, ∞). The number on the left side is the lower bound and the right side is the upper bound. This notation means from 3 up to infinity. In addition, the symbol ( denotes that 3 is not included in the solution. Therefore, the interval (5,7) means all real numbers from 5 to 7, not including 5 and 7. The infinity symbol always takes the ( and ) symbols.  » Read more