# Number Line Calculator + Online Solver With Free Steps

The **Number Line Calculator** is used to calculate the integer solutions of an inequality interval and displays it on the number line. It takes an interval of the values of **x** as input and outputs the integers which lie in **between the interval**.

It works by using the two inequalities: **less than** “**<**” and **greater than** “**>**”. The calculator can take any interval from the set of integers **Z** and display the solution on the number line.

The set of **integers** **Z** can be represented as follows:

**Z = [ { …,-4,-3,-2,-1,0,1,2,3,4,… } ] **

An **interval** on the number line can be defined as follows:

**a < x < b**

Where **a** is the** lower value** and **b** is the **upper value** of the interval. Both a and b are integer values. The inequality shows that x is greater than a and less than b.

The calculator computes the **integer solutions** which lie between a and b.

## What Is a Number Line Calculator?

**The Number Line Calculator is an online tool that is used to calculate the integer solution of an interval of x defined by two inequalities. It also displays the integer interval on the Number Line.**

## How To Use the Number Line Calculator

The user can use the Number Line Calculator by following the steps given below.

### Step 1

The user must first enter the **integer interval** defined by the two inequalities in the calculator’s input window.

The interval {a < x < b } shows that **x** is greater than the integer** a** and less than the integer **b**.

The interval { a > x > b } shows that **x** is less than **a** and greater than** b**.

For the **default** example, the calculator shows the inequality interval to be { 2 < x < 7}.

### Step 2

The user must now press the “**Submit**” button of the Number Line Calculator. The calculator processes the input interval of integer values and computes the output as follows.

### Output

The calculator displays the output in the five windows given below.

#### Input Interpretation

The calculator processes the **input** and displays it in this window. It shows the inequality interval entered by the user.

For the **default** example, the calculator shows the input interpretation as follows:

**Number Line = 2 < x < 7 **

#### Number Line

The calculator displays the input interval on the **number line** in this window. The Number Line is a line representing the set of integers placed at **regular **intervals.

The interval { a < x < b } is represented by drawing a **line** from a to b and the interval { a > x > b } is displayed by drawing a line from b to a on the **number line**.

For the **default** example, the interval { 2 < x < 7 } is represented on the number line as shown in figure 1.

#### Solution

The Solutions window displays the interval { a < x < b } or { a > x > b } as entered by the user. For the **default** example, the Solution is:

2 < x < 7

#### Interval Notation

The calculator shows the interval notation of the entered integer interval in this window.

The interval notation is represented by the **lower value** on the left-hand side and the **upper value** on the right-hand side separated by a comma in parenthesis.

For the **default** inequality interval, the calculator shows the Interval Notation as follows:

Interval Notation = ( 2,7 )

#### Integer Solutions

The Integer Solutions shows all the **solutions** for the inequality interval entered by the user. The integer solutions for the interval { a < x < b } or { a > x > b } lie in-between a and b or b and a respectively.

The calculator displays the integer values of x for the **default** example { 2 < x < 7 } as follows:

x = 3

x = 4

x = 5

x = 6

## Solved Examples

The following examples are solved through the Number Line Calculator.

### Example 1

An inequality interval is given by:

5 > x > -4

Show the above interval on the **number line**, write the interval notation and compute all the integer solutions.

### Solution

The user must first enter the inequality interval { 5 > x > -4 } in the calculator’s input window. After submitting the input, the calculator shows the **Input Interpretation** as follows:

Number Line = 5 > x > – 4

The calculator shows the above interval on the** Number Line** shown in figure 2. A line is drawn from -4 to 5 on the number line.

The Number Line calculator displays the **Solution** for the input interval as follows:

– 4 < x < 5

The **Interval Notation** shown in the calculator’s output window is as follows:

Interval Notation = ( – 4,5 )

The **Integer Solutions** for the interval { 5 > x > -4 } are:

x = pm 3

x = pm 2

x = pm 1

x = 0

x = 4

### Example 2

For the interval where **x** is less than **6** and greater than **1**, represent the interval by using the inequality symbol, show it on the **number line**, display the interval notation and calculate the integer solutions for the given interval.

### Solution

The example can be written as an inequality interval as follows:

1 < x < 6

The user must first enter the above integer interval in the input tab of the calculator.

After entering the interval, the user must press “**Submit**” for the calculator to compute the result and display the **output** as given below.

The calculator shows the **Input Interpretation** which is the input interval entered by the user. For this example, the input is:

Number Line = 1 < x < 6

The calculator shows the **Number Line** with a line drawn from 1 to 6 for the interval { 1 < x < 6 }. It is shown in figure 3 as follows:

The **Solution** for the input interval displayed by the calculator is as follows:

1 < x < 6

The calculator also displays the **Interval Notation** which shows the **lower value** 1 and the **upper value** 6 for the given example. It is displayed as follows:

Interval Notation = ( 1,6 )

The **Integer Solutions** shows all the values of **x** which lie in between the interval { 1 < x < 6 }. They are displayed by the calculator as follows:

x = 2

x = 3

x = 4

x = 5