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Interval Notation Calculator

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The numbers that are between the two numbers is an interval. For example, $1 < x \leq 7$ , interval are all the numbers that lies from 1 to 7. Interval can be positive and negative numbers. Interval notation is representing a pair of numbers as an inequality. Interval can be of different types,

1. Open interval, represented as (a, b).
2. Closed interval, represented as [a, b].
3. Half open interval or half closed interval, represented as (a, b] or [a, b).

Here, a and b are any real numbers.

Taking the above example $1 < x \leq 7$ or (1, 7], interval is shown below in the number line.
Interval Notation
 

Steps

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Step 1 : Note the given interval.

Step 2 : Write down the inequality for the given interval.

Step 3 : Draw the number line for the inequality.
  • Use open circle if the inequality is $< or >$.
  • Use close circle if the inequality is $\leq or \geq $ .

Problems

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Below are some of the problems based on interval notation.

Solved Examples

Question 1: Draw number line for the interval [0, 3).
Solution:
 
Step 1 : Given interval: [0, 3)

Step 2 : Inequality for the interval is,
0 $\leq x$ < 3

Step 3 : Number line for the interval [0, 3) is,
Interval Notation Problem

 

Question 2: Draw number line for the interval (2, 5).
Solution:
 
Step 1 : Given interval: (2, 5)

Step 2 : Inequality for the interval is,
2 < x < 5

Step 3 : Number line for the interval (2, 5) is,
Problem on Interval Notation