Interval notation is expressing the inequality in terms of interval containing a pair of numbers. These pair represents the starting and end point and the interval tells us whether end points are included or excluded in the number line.

If a and b are given real numbers then they can be expressed by the intervals namely
Open Interval: It is represented as $(a, b)$ = $\{ x\ \epsilon\ R\ |\ a < x < b \}$

Closed Interval: It is represented as $[a, b]$ = $\{x\ \epsilon\ R\ |\ a \leq x \leq b \}$,

Half Open Interval: It is represented as $(a, b]$ = $\{x\ \epsilon\ R\ |\ a < x \leq b \}$ or $[a, b)$ = $\{ x\ \epsilon\ R\ |\ a \leq x < b \}$.
Interval Notation Calculator represents the interval in terms of inequality and plots its graph on number line. The ( ) braces representing open interval gives open circle and [ ] braces representing closed interval gives closed circle on the graph.

## Interval Notation Problems

Step 1: Read the problem and observe the given interval, express the intervals in terms of inequality.

Step 2 : Plot the graph on the number line using the inequality.
1. If in inequality < or > symbols are there then use open circle and
2. If in inequality $\leq$ or $\geq$ are there then use closed circle.

Below are given some solved problems on Interval notation which may be helpful for you.

### Solved Examples

Question 1: Plot interval (0, 3) on the number line.
Solution:

Step 1: The given interval is (0, 3). The inequality notation is given by 0 $\leq$ x < 3. Hence the integer solutions are
x = 0
x = 1
x = 2

Step 2 : Hence the graph will have close circle at 0 and open circle at 3.

Question 2: Plot interval (-1, 6) on the number line.
Solution:

Step 1: The given interval is (-1, 6). The inequality notation is given by -1 < x $\leq$ 6. Hence the integer solutions are
x = 0
x = 1
x = 2
x = 3
x = 4
x = 5
x = 6

Step 2 : Hence the graph will have open circle at -1 and closed circle at 6.

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