Solving and Graphing Linear Inequalities: A Comprehensive Guide

Algebra 1 Grades High School 2:54 Video
Print Lesson Plan Watch Video

Lesson Description

Learn how to solve linear inequalities involving multiplication and division, with a focus on remembering to flip the inequality sign when multiplying or dividing by a negative number. Also, understand how to graph the solution set on a number line.

Video Resource

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

Khan Academy

Duration: 2:54
Watch on YouTube

Key Concepts

  • Solving linear inequalities using multiplication and division.
  • Flipping the inequality sign when multiplying or dividing by a negative number.
  • Graphing the solution set of a linear inequality on a number line.

Learning Objectives

  • Students will be able to solve linear inequalities involving multiplication and division.
  • Students will be able to correctly flip the inequality sign when necessary.
  • Students will be able to represent the solution set of a linear inequality on a number line.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the basic properties of inequalities and the concept of solving equations. Briefly discuss the differences between equations and inequalities.
  • Video Instruction (10 mins)
    Play the Khan Academy video 'Multiplying and dividing with inequalities example | Linear inequalities | Algebra I | Khan Academy'. Encourage students to take notes on the key steps and concepts presented in the video.
  • Guided Practice (15 mins)
    Work through example problems similar to those in the video, emphasizing the importance of flipping the inequality sign when multiplying or dividing by a negative number. Have students solve problems on the board or in small groups.
  • Independent Practice (15 mins)
    Assign students a set of practice problems to solve independently. Circulate to provide support and answer questions.
  • Wrap-up and Assessment (5 mins)
    Review the key concepts and address any remaining questions. Administer a short quiz or exit ticket to assess student understanding.

Interactive Exercises

  • Inequality Sort
    Provide students with a set of inequalities, some of which require flipping the sign. Have them sort the inequalities into two groups: those that require flipping and those that do not.
  • Graphing Game
    Use an online tool or whiteboard to create a graphing activity where students graph solutions to linear inequalities on a number line.

Discussion Questions

  • Why is it necessary to flip the inequality sign when multiplying or dividing by a negative number?
  • How does graphing the solution set help visualize the solutions to an inequality?
  • Can you think of real-world situations that can be modeled using linear inequalities?

Skills Developed

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

Multiple Choice Questions

Question 1:

Solve the inequality: -3x < 12

Correct Answer: x > -4

Question 2:

When do you need to flip the inequality sign when solving?

Correct Answer: Multiplying by a negative number

Question 3:

Which of the following represents the solution to x ≥ -2 on a number line?

Correct Answer: A closed circle at -2 with shading to the right

Question 4:

Solve the inequality: 5x > -25

Correct Answer: x > -5

Question 5:

Which number is a solution to the inequality x ≤ 3?

Correct Answer: 3

Question 6:

Solve for x: -2x ≥ -8

Correct Answer: x ≤ 4

Question 7:

The solution set to an inequality is graphed with an open circle. This indicates:

Correct Answer: The value is not included in the solution

Question 8:

Solve: x / -4 < 2

Correct Answer: x > -8

Question 9:

Which inequality represents 'a number is greater than or equal to 5'?

Correct Answer: x ≥ 5

Question 10:

What is the first step in solving -4x + 2 > 10?

Correct Answer: Subtract 2 from both sides

Fill in the Blank Questions

Question 1:

When multiplying or dividing an inequality by a __________ number, you must flip the inequality sign.

Correct Answer: negative

Question 2:

The inequality x > 5 means x is __________ than 5.

Correct Answer: greater

Question 3:

The solution to -x < 3 is x __________ -3.

Correct Answer: greater than

Question 4:

On a number line, a __________ circle indicates the value is included in the solution.

Correct Answer: closed

Question 5:

The opposite of multiplying is __________.

Correct Answer: dividing

Question 6:

When graphing x ≤ 7, you shade to the __________ on the number line.

Correct Answer: left

Question 7:

Solving inequalities is similar to solving __________.

Correct Answer: equations

Question 8:

The inequality sign '>' means __________.

Correct Answer: greater than

Question 9:

If 2x < 8, then x < __________.

Correct Answer: 4

Question 10:

The inequality x ≥ -1 means x is greater than or __________ to -1.

Correct Answer: equal

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

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans