Solve the inequality in interval notation calculator

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Solve inequalities

This calculator will try to solve the linear, quadratic, polynomial, rational, and absolute value inequalities. It can handle compound inequalities and systems of inequalities as well.

To graph inequalities, use the graphing calculator.

Your input: solve $$$2 \lt \left|{x - 1}\right| \leq 4$$$

Answer

Answer: $$$\left[-3, -1\right) \cup \left(3, 5\right]$$$

Approximate Form: $$$\left[-3, -1\right) \cup \left(3, 5\right]$$$

Interval Notation Calculator calculates the length of the interval between any two numbers and expresses the inequality based on the selected topology. Further, the interval is also represented on a number line.

What is Interval Notation Calculator?

Interval Notation Calculator is an online tool that helps to display the given interval on a number line, represents the inequality according to the specified topology, and calculates the length of the interval between the two given numbers. To use the interval notation calculator, enter the values in the input boxes.

Interval Notation Calculator

How to Use Interval Notation Calculator?

Follow the steps given below to find the length of the interval, its number line representation, and the inequality based on the given topology using the online interval notation calculator.

• Step 1: Go to Cuemath's online interval notation calculator.
• Step 2: Select the topology from the drop-down list and enter the numbers in the given input boxes.
• Step 3: Click on the "Calculate" button to calculate the length, give the number line representation and the inequality of the interval.
• Step 4: Click on the "Reset" button to clear the fields and enter new values.

How Does Interval Notation Calculator Work?

Interval notation is used to represent the set of real numbers that lie between any two given real numbers. Inequalities can be represented with the help of intervals There are four main types of intervals. Suppose we have two endpoints x and y, where x < y, then the intervals can be classified as follows:

1. Open Interval

In this, the two endpoints are not included. If we have a number, z, that lies between x and y then the inequality is denoted as x < z < y. An open interval is expressed using round brackets, i.e., (x, y).

2. Closed Interval

Both the endpoints are included in this interval. The inequality can be given as x ≤ z ≤ y. Square brackets are used to express closed intervals, i.e., [x, y].

3. Half Closed Right Interval

In this type of interval, only the left endpoint is included while the right endpoint is excluded. x ≤ z < y is the inequality. The left side uses a square bracket while the right side of the interval uses a round bracket, i.e., [x, y).

4. Half Closed Left Interval

Only the right endpoint is included while the left is excluded in this interval. x < z ≤ y will be the inequality. The left side uses a round bracket while the right side will have a square bracket, i.e., (x, y].

Length of the interval between the endpoints x and y can be calculated as follows:

Length = y - x.

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Solved Examples on Interval Notation Calculator

Example 1:

Plot the interval [2, 4] on the number line, specify the inequality, topology and calculate its length. Verify the results using the online interval notation calculator.

Solution:

Number Line :

Inequality = 2 ≤ x ≤ 4

Topology = Closed Interval

Length = 4 - 2 = 2

Example 2:

Plot the interval [-3, 1) on the number line, specify the inequality, topology and calculate its length. Verify the results using the online interval notation calculator.

Solution:

Number Line :

Inequality = -3 ≤ x < 1

Topology = Left closed right open

Length = 1 - (-3) = 4

Similarly, you can use the interval notation calculator to find the number line representation, inequalities, topologies, and the length for the following intervals:

• (-2, 5]
• (5, 9)

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• Interval Notation
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