Explanation:
A number line is a horizontal line constructed with integers marked at equal distances from one another. It is extended infinitely on both sides unless specified otherwise. The purpose of a number line is to show real numbers diagrammatically and to solve mathematical operations.
When any number is graphed on such a line, the point corresponding to it is marked distinctly. For example:
The above number line is used to express the positive integer 2.
Inequalities can also be graphed on number lines in a similar manner. However, since these include the greater than (>), less than ( or < symbol, an open circle is used at the location of the number in the inequality. On the other hand, when an inequality has the ≥ or ≤ symbol, a closed circle is used at the position of the number. In both cases, a dark line is drawn from the circle in the appropriate direction to show the solutions of the inequality.
For instance, consider the inequality x ≤ 4. It can be expressed on a number line by drawing a closed circle at 4 and then marking a dark line that extends infinitely to its left.
Similarly, if the inequality is x >1 , it can be indicated on a number line with an open circle at 1 and a dark line that extends infinitely to the right of 1.
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