Graphing Inequalities on a Number Line

🔑 Key Concepts

  • Solve the inequality first before graphing the solution on a number line.
  • A closed circle means the endpoint is included, so use \( \le \) or \( \ge \).
  • An open circle means the endpoint is not included, so use \( < \) or \( > \).
  • Shade left for values less than a number and shade right for values greater than a number.
  • If you divide or multiply both sides by a negative number, reverse the inequality symbol.

✏️ Worked Examples — Solve Then Match the Graph

🧠 Math Vocabulary

  • Inequality: A mathematical statement that compares two quantities using symbols such as \( < \), \( > \), \( \le \), or \( \ge \).
  • Closed Circle: A point on a number line that shows the endpoint is included in the solution.
  • Open Circle: A point on a number line that shows the endpoint is not included in the solution.
  • Graph a Solution: Represent all values that make an inequality true on a number line.
  • Reverse the Inequality: Change the direction of the inequality symbol when multiplying or dividing by a negative number.

💡 Main Idea

To graph an inequality on a number line, first solve the inequality so the variable is isolated. Then decide whether the endpoint is included or not, and determine whether the graph should extend to the left or to the right. The inequality symbol tells you the direction, and the type of circle tells you whether the endpoint is part of the solution.

📚 What You Should Already Know

Before graphing inequalities, you should be comfortable solving one-step and two-step inequalities, using inverse operations, and recognizing when an inequality sign must be reversed after dividing by a negative number. You should also know how to read a number line and identify integer values.

🚀 What Comes Next

After graphing one-variable inequalities on a number line, the next step is writing inequalities from graphs and then moving into compound inequalities and systems of inequalities. These skills help connect symbolic solutions to visual models.

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