1D Linear Inequalities Graphing Calculator

Graph single or multiple inequalities of the form x < a, x ≤ b, x > c, x ≥ d on a number line.

Solution & Number Line

📘 About the 1D Linear Inequalities Graphing Calculator

This interactive calculator helps you graph single or multiple linear inequalities on a number line. It supports all standard inequality operators: <, , >, and , and provides instant visual feedback with shaded regions and boundary points.

🔢 Multiple Inequalities

Easily enter one or more inequalities at once.

  • Single inequality: x < a
  • Multiple inequalities: x > b and x ≤ c

The calculator automatically plots all inequalities on the same number line.

📊 Visual Number Line

The calculator draws a number line showing:

  • Boundary points (open or closed)
  • Shaded regions representing solution sets

This makes it simple to see where the inequalities hold true.

✍️ Step-by-Step Calculation

As you type your inequalities:

  • The boundary values are calculated
  • Open or closed circles are displayed correctly
  • The correct shading direction is applied

You can instantly verify and understand the solution set.

⚡ Instant & Beginner Friendly

The graph updates in real time as you type. Perfect for students, homework, and exam preparation — no manual plotting needed.

⚙️ How the Calculator Works

1️⃣ Select the number of inequalities you want to graph (1–5), then enter each inequality with its operator and value.

2️⃣ The calculator plots a horizontal number line as the coordinate axis.

3️⃣ For each inequality:

  • The boundary point is placed at x = value.
  • Open circles indicate < or >, closed circles indicate ≤ or ≥.
  • The region satisfying the inequality is shaded accordingly.

4️⃣ When multiple inequalities are entered, all solution sets are displayed together on the same number line for easy comparison.

5️⃣ Use the "Clear All" button to reset inputs, or "Reload Calculator" to reset everything and start fresh.

📐 Linear Inequality Formula Explained

A linear inequality represents all numbers that make a linear expression true. It can have one of the following forms: x < a, x ≤ a, x > a, or x ≥ a. These inequalities describe which points lie to the left or right of a boundary point on a number line.

Solution Region: x ≷ a

In this formula:

  • x – The variable whose values we are finding.
  • a – The boundary value that divides the number line.
  • – The inequality sign: <, , >, or .
  • Solution region – The set of all x-values that satisfy the inequality.

For each inequality:

  • Boundary point: The value of a is marked on the number line.
  • Open circle: Used for < or >, meaning a is not included.
  • Closed circle: Used for or , meaning a is included.
  • Shaded region: Indicates all numbers x that satisfy the inequality.

For example, if you have:

x ≥ 3

The solution set is all numbers greater than or equal to 3. On the number line:

  • A closed circle is placed at x = 3.
  • The region to the right of 3 is shaded.

This simple formula and visualization technique allows students and users to quickly understand and graph any 1D linear inequality. It is the foundation for more complex topics like compound inequalities and interval notation, making it perfect for homework, exams, or self-study.

📌 Example

Suppose you enter:

x ≥ 2 and x < 5

The calculator displays:

A number line with a closed circle at 2, an open circle at 5, and the region between 2 and 5 shaded.

This represents all real numbers x such that 2 ≤ x < 5.

Frequently Asked Questions About the
1D Linear Inequalities Graphing Calculator

Everything you need to know about graphing linear inequalities on a number line quickly and accurately.

What does this calculator do?

This calculator allows you to graph **one or multiple linear inequalities** on a 1D number line. For each inequality, it automatically:

  • Places the boundary point at the correct value.
  • Shows an open circle for strict inequalities (< or >) or a closed circle for inclusive inequalities (≤ or ≥).
  • Shades the region representing all numbers that satisfy the inequality.

This visual representation helps you **instantly see the solution set without manual plotting.

Is this calculator free?

Yes! The calculator is **completely free to use**, with **no registration required** and **no hidden fees**. You can access all features directly from your browser.

Can it handle multiple inequalities at once?

Yes! You can enter up to **5 inequalities at the same time**. The calculator plots each inequality on the **same number line**, applying:

  • Correct boundary types (open or closed circles).
  • Shading for each solution region.

This makes it easy to compare multiple inequalities and see how their solution sets overlap.

What do the open and closed circles mean?

  • Open circle: For strict inequalities (< or >), the boundary value is not included in the solution set.
  • Closed circle: For inclusive inequalities (≤ or ≥), the boundary value is included in the solution set.

These symbols make it easy to understand which numbers satisfy each inequality at a glance.

Can I see the solution region visually?

Absolutely! The calculator **shades all x-values that satisfy the inequality**, so you can immediately see:

  • The start and end of the solution region.
  • Whether boundary points are included or excluded.
  • Overlapping solution areas when multiple inequalities are present.

This makes it **much faster and easier** than manually plotting.

Can I clear or reset the calculator?

Yes! You can:

  • Click **"Clear All"** to reset only the input fields.
  • Click **"Reload Calculator"** to reset everything, including the number of inequalities and the graph, starting fresh.
  • This allows you to experiment with multiple examples easily.

Is this suitable for students and exam prep?

Definitely! It is designed for **homework, quizzes, and exam practice**, providing:

  • Instant, accurate number line graphs.
  • Clear visualization of solution regions.
  • Understanding of boundary points and inequalities.
  • This makes it a valuable tool for both learning and revision.

Can I use it on mobile devices?

Yes, the calculator is **fully responsive**. It works smoothly on:

  • Smartphones
  • Tablets
  • Laptops and desktops
  • You can graph inequalities and see solution regions on any device without losing functionality.

How do I enter inequalities?

To enter inequalities:

  • Select the number of inequalities you want to graph (1–5).
  • Choose the operator (<, ≤, >, ≥) from the dropdown for each inequality.
  • Enter the corresponding numerical value.
  • The graph updates **automatically** as you type.
  • This makes input fast and interactive.

Does it support compound intervals?

Yes! The calculator can handle:

  • Overlapping inequalities
  • Multiple solution regions
  • It combines all inequalities and shows the **correct overall solution regions on the number line.

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