Graphing Inequalities on a Number Line: Visualizing Solutions

Algebra 1 Grades High School 1:34 Video
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Lesson Description

Learn how to represent linear inequalities on a number line. This lesson covers identifying solutions and representing them graphically.

Video Resource

Example of plotting a simple inequality on a number line | Pre-Algebra | Khan Academy

Khan Academy

Duration: 1:34
Watch on YouTube

Key Concepts

  • Inequalities
  • Number Lines
  • Graphical Representation of Solutions
  • Open and Closed Intervals

Learning Objectives

  • Students will be able to represent linear inequalities on a number line.
  • Students will be able to differentiate between strict inequalities (less than, greater than) and inclusive inequalities (less than or equal to, greater than or equal to) when graphing.
  • Students will be able to interpret a number line graph to determine the solution set of an inequality.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic inequality symbols (<, >, ≤, ≥) and their meanings. Discuss the concept of a solution set for an inequality - that is, all the values that make the inequality true.
  • Video Presentation (5 mins)
    Play the Khan Academy video "Example of plotting a simple inequality on a number line". Encourage students to take notes on the key steps: drawing the number line, using open or closed circles, and shading the solution region.
  • Guided Practice (10 mins)
    Work through a few example problems together. Start with inequalities like x > 2, x ≤ -1, and x < 5. Emphasize the importance of the open circle for strict inequalities and the closed circle for inclusive inequalities. Clearly demonstrate how to shade the number line in the correct direction to represent all the solutions.
  • Independent Practice (10 mins)
    Provide students with a worksheet containing a variety of linear inequalities. Have them graph each inequality on a number line. Circulate the room to provide assistance and answer questions.
  • Review and Discussion (5 mins)
    Review the answers to the independent practice problems. Address any common mistakes or misconceptions. Discuss how graphing inequalities on a number line helps visualize the solution set.

Interactive Exercises

  • Number Line Drag and Drop
    Provide students with a digital number line and a set of inequality symbols and numbers. Have them drag and drop the correct symbols and numbers onto the number line to represent given inequalities.
  • Inequality Matching Game
    Create a matching game where students match inequalities with their corresponding number line graphs.

Discussion Questions

  • Why is it important to use an open circle for strict inequalities and a closed circle for inclusive inequalities?
  • How does graphing an inequality on a number line help us understand the solution set?
  • Can you give a real-world example of a situation that can be represented by an inequality?

Skills Developed

  • Visual Representation of Mathematical Concepts
  • Problem-Solving
  • Critical Thinking
  • Understanding of Inequality Symbols

Multiple Choice Questions

Question 1:

Which symbol represents 'less than or equal to'?

Correct Answer: ≤

Question 2:

When graphing x > 3 on a number line, what type of circle should be used at 3?

Correct Answer: Open circle

Question 3:

Which of the following values is a solution to the inequality x < 5?

Correct Answer: 4

Question 4:

What does shading to the left on a number line represent when graphing an inequality?

Correct Answer: Values less than

Question 5:

Which inequality is represented by a closed circle at -2 and shading to the right?

Correct Answer: x ≥ -2

Question 6:

Which of the following is NOT a solution to x ≥ 0?

Correct Answer: -1

Question 7:

What is the first step in graphing an inequality on a number line?

Correct Answer: Draw the number line

Question 8:

If you have the inequality x ≤ 7, do you fill in the circle at 7?

Correct Answer: Yes

Question 9:

What does the greater than symbol look like?

Correct Answer: >

Question 10:

In the inequality x > 10, is 10 a possible answer?

Correct Answer: No

Fill in the Blank Questions

Question 1:

The symbol '>' means ________ than.

Correct Answer: greater

Question 2:

When graphing x < 4, you use an ______ circle at 4.

Correct Answer: open

Question 3:

The solution set of an inequality includes all the _______ that make the inequality true.

Correct Answer: values

Question 4:

A ______ circle is used to show that a number is included in the solution set.

Correct Answer: closed

Question 5:

x ≥ -3 means x is greater than or ______ to -3.

Correct Answer: equal

Question 6:

When graphing x < -1 you shade to the ______.

Correct Answer: left

Question 7:

The symbol '≤' means less than or _______ to.

Correct Answer: equal

Question 8:

If the circle is filled in on the number line, the value is ________.

Correct Answer: included

Question 9:

If x > 5, then x could be ____.

Correct Answer: 6

Question 10:

When graphing x ≥ 2, you would shade to the _______.

Correct Answer: right

Educational Standards

A1.A.2.1:Represent relationships using mathematical models with linear inequalities; solve the resulting inequalities, graph on a coordinate plane, and interpret the solutions. A1.A.2.2:Represent relationships using mathematical models with compound and absolute value inequalities and solve the resulting inequalities by graphing and interpreting the solutions on a number line.

Teaching Materials

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