Flipping the Script: Solving Inequalities with Multiplication and Division

Algebra 1 Grades High School 10:27 Video
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Lesson Description

Learn how to solve linear inequalities involving multiplication and division, with a special focus on when and why you need to 'flip' the inequality sign. We'll also explore different ways to represent the solution set, including interval notation and set notation.

Video Resource

Multiplying and dividing with inequalities | Linear inequalities | Algebra I | Khan Academy

Khan Academy

Duration: 10:27
Watch on YouTube

Key Concepts

  • Solving linear inequalities
  • The multiplication/division property of inequality (flipping the sign when multiplying or dividing by a negative number)
  • Representing solutions using number lines, interval notation, and set notation

Learning Objectives

  • Students will be able to solve linear inequalities involving multiplication and division.
  • Students will be able to correctly apply the multiplication/division property of inequality by flipping the inequality sign when multiplying or dividing by a negative number.
  • Students will be able to represent the solution set of an inequality using number lines, interval notation, and set notation.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic rules for solving equations. Emphasize that the goal is to isolate the variable. Briefly discuss the difference between equations and inequalities. Ask students for examples of when inequalities might be used in real life (e.g., speed limits, budget constraints).
  • Video Viewing and Note-Taking (15 mins)
    Play the Khan Academy video 'Multiplying and dividing with inequalities'. Instruct students to take notes on the key steps involved in solving inequalities, paying close attention to the rule about flipping the inequality sign when multiplying or dividing by a negative number. Encourage them to write down the examples worked through in the video.
  • Guided Practice (15 mins)
    Work through several example problems on the board, similar to those presented in the video. Emphasize the importance of showing all steps and checking the solution. Include examples that require flipping the inequality sign and those that do not. Discuss the different ways to represent the solution set (number line, interval notation, set notation) and practice converting between them.
  • Independent Practice (10 mins)
    Provide students with a set of practice problems to solve independently. Circulate around the room to provide assistance as needed. Encourage students to work together and discuss their solutions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts covered in the lesson. Administer a short quiz to assess student understanding.

Interactive Exercises

  • Number Line Representation
    Provide students with a variety of inequalities and have them represent the solution sets on a number line. Include open and closed circles to indicate whether the endpoint is included or excluded.
  • Interval Notation Conversion
    Give students inequalities and ask them to write the solution set in interval notation. Then, provide interval notation and have them write the corresponding inequality.

Discussion Questions

  • Why is it necessary to flip the inequality sign when multiplying or dividing by a negative number?
  • Can you think of a real-world situation where solving an inequality would be useful?
  • What are the advantages and disadvantages of using each of the different notations for representing solution sets (number line, interval notation, set notation)?

Skills Developed

  • Problem-solving
  • Critical thinking
  • Algebraic manipulation
  • Mathematical representation

Multiple Choice Questions

Question 1:

What happens to the inequality sign when you multiply or divide both sides of an inequality by a negative number?

Correct Answer: It flips.

Question 2:

Solve the inequality: -2x < 6

Correct Answer: x > -3

Question 3:

Which of the following is the interval notation for x ≥ 5?

Correct Answer: [5, ∞)

Question 4:

Solve the inequality: x / -3 > 4

Correct Answer: x < -12

Question 5:

What does a bracket '[' or ']' in interval notation indicate?

Correct Answer: The endpoint is included.

Question 6:

Which inequality is represented by the interval notation (-∞, 2)?

Correct Answer: x < 2

Question 7:

Solve for x: -0.5x ≥ 7.5

Correct Answer: x ≤ -15

Question 8:

What is the solution to x/ -5 < -2?

Correct Answer: x > 10

Question 9:

If you multiply both sides of -x > 5 by -1, what is the resulting inequality?

Correct Answer: x < -5

Question 10:

Which notation represents all real numbers greater than or equal to -3?

Correct Answer: [-3, ∞)

Fill in the Blank Questions

Question 1:

When multiplying or dividing an inequality by a negative number, you must ___________ the inequality sign.

Correct Answer: flip

Question 2:

The interval notation [a, b] means that both 'a' and 'b' are __________ in the solution set.

Correct Answer: included

Question 3:

The solution to -x > 4 is x ___________ -4.

Correct Answer: <

Question 4:

If x/-2 < 5, then x ___________ -10.

Correct Answer: >

Question 5:

The set of all numbers greater than 2 can be written as (2, ___________).

Correct Answer: ∞

Question 6:

In the inequality 3x > -9, dividing both sides by 3 gives x __________ -3.

Correct Answer: >

Question 7:

The symbol '∞' in interval notation always uses a ___________.

Correct Answer: parenthesis

Question 8:

The inequality -x/4 ≤ 2 simplifies to x _______ -8

Correct Answer: ≥

Question 9:

When graphing an inequality on a number line, use a(n) _________ circle if the value is not included in the solution.

Correct Answer: open

Question 10:

The solution set {x | x ≥ -5} can be written in interval notation as [__________, ∞).

Correct Answer: -5

Educational Standards

A1.A.2:Represent and solve real-world and mathematical problems using linear inequalities and compound inequalities; interpret solutions in the original context. 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.

Teaching Materials

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