Solving Compound Inequalities with 'OR' (Disjunction)

Algebra 2 Grades High School 7:17 Video
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Lesson Description

Learn how to solve compound inequalities involving the 'OR' condition and represent their solutions on a number line. This lesson covers the concept of disjunction and provides step-by-step examples.

Video Resource

Compound Inequalities on a Number Line | OR

Kevinmathscience

Duration: 7:17
Watch on YouTube

Key Concepts

  • Compound Inequalities
  • Disjunction (OR)
  • Number Line Representation
  • Solving Inequalities

Learning Objectives

  • Students will be able to solve compound inequalities connected by 'OR'.
  • Students will be able to represent the solution set of a compound inequality on a number line.
  • Students will be able to correctly identify open and closed circles on the number line based on inequality symbols.
  • Students will be able to interpret the meaning of the solution set in the context of the original inequality.

Educator Instructions

  • Introduction (5 mins)
    Begin by introducing the concept of compound inequalities and distinguishing them from simple inequalities. Explain that this lesson will focus specifically on inequalities connected by the word 'OR', also known as disjunctions. Briefly review the symbols for inequalities (<, >, ≤, ≥) and their corresponding representation on a number line (open vs. closed circles).
  • Video Viewing and Note-Taking (15 mins)
    Play the Kevinmathscience video 'Compound Inequalities on a Number Line | OR'. Instruct students to take notes on the steps for solving compound inequalities with 'OR' and how to graph the solutions on a number line. Encourage them to pay attention to the examples provided in the video.
  • Guided Practice (15 mins)
    Work through a few example problems together as a class. Start with simpler inequalities and gradually increase the complexity. Emphasize the importance of solving each inequality separately and then combining the solutions on the number line. Reinforce the use of open and closed circles and the direction of the arrows.
  • Independent Practice (10 mins)
    Provide students with a set of practice problems to solve independently. Circulate around the classroom to provide assistance and answer questions. After the allotted time, review the answers as a class, addressing any common mistakes or misconceptions.
  • Wrap-up and Discussion (5 mins)
    Summarize the key concepts covered in the lesson. Reiterate the steps for solving and graphing compound inequalities with 'OR'. Open the floor for any remaining questions or clarifications.

Interactive Exercises

  • Number Line Race
    Divide the class into teams. Present a compound inequality. The first team to correctly solve the inequality and graph the solution on a large number line drawn on the board wins a point.
  • Error Analysis
    Present students with worked-out solutions to compound inequalities, some of which contain errors. Students must identify the errors and correct them.

Discussion Questions

  • How does solving a compound inequality with 'OR' differ from solving a single inequality?
  • What does the solution set of a compound inequality with 'OR' represent?
  • Explain the difference between using an open circle and a closed circle on the number line.
  • Can a number be a solution to only one part of an 'OR' compound inequality and still be part of the overall solution?

Skills Developed

  • Algebraic Manipulation
  • Problem Solving
  • Graphical Representation
  • Critical Thinking

Multiple Choice Questions

Question 1:

Which of the following represents the solution to 'x < 2 OR x > 5'?

Correct Answer: All real numbers less than 2 or greater than 5

Question 2:

What type of circle is used on a number line to represent '> ' or '<'?

Correct Answer: Open circle

Question 3:

What does 'OR' mean in the context of compound inequalities?

Correct Answer: At least one of the inequalities must be true.

Question 4:

Solve: 'x + 3 < 1 OR x - 2 > 4'

Correct Answer: x < -2 OR x > 6

Question 5:

Which number line represents 'x ≤ -1 OR x ≥ 3'?

Correct Answer: A number line with closed circles at -1 and 3, shading outwards

Question 6:

What is another term for a compound inequality using 'OR'?

Correct Answer: Disjunction

Question 7:

Solve: '2x < -4 OR x + 5 > 7'

Correct Answer: x < -2 OR x > 2

Question 8:

What is the first step when solving a compound inequality with 'OR'?

Correct Answer: Solve each inequality separately.

Question 9:

Which of the following represents a number that satisfies 'x < -5 OR x > 0'?

Correct Answer: -6

Question 10:

Which symbol indicates that the endpoint IS included in the solution set?

Correct Answer: ≤

Fill in the Blank Questions

Question 1:

A compound inequality using 'OR' is called a(n) ________.

Correct Answer: disjunction

Question 2:

On a number line, a(n) ________ circle represents that the endpoint is NOT included in the solution.

Correct Answer: open

Question 3:

The solution to a compound inequality with 'OR' includes all numbers that satisfy ________ of the inequalities.

Correct Answer: at least one

Question 4:

To solve a compound inequality with 'OR', you should solve ________ inequality separately.

Correct Answer: each

Question 5:

If x < 3 OR x > 7, the solution set includes all numbers less than 3 ________ all numbers greater than 7.

Correct Answer: and

Question 6:

The symbol '≤' means less than or ________.

Correct Answer: equal

Question 7:

When graphing 'x > 5', the arrow on the number line points to the ________.

Correct Answer: right

Question 8:

The numbers that are NOT part of the solution to 'x < -1 OR x > 1' are those between -1 ________ 1 inclusive.

Correct Answer: and

Question 9:

If a number satisfies both parts of an 'OR' inequality, it is ________ part of the overall solution.

Correct Answer: still

Question 10:

On a number line, a solid circle indicates that the endpoint ________ included in the solution set.

Correct Answer: is

Educational Standards

A2.A.1.9:Solve systems of linear inequalities in two variables, with a maximum of three inequalities; graph and interpret the solutions on a coordinate plane. Graphing calculators or other appropriate technology may be used. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

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