Mastering Absolute Value Equations: A Step-by-Step Guide

Algebra 2 Grades High School 16:20 Video
Print Lesson Plan Watch Video

Lesson Description

Learn to solve absolute value equations with confidence! This lesson covers isolating absolute values and applying the fundamental principle of two possible solutions.

Video Resource

How to Solve Absolute Value Equations Algebra

Kevinmathscience

Duration: 16:20
Watch on YouTube

Key Concepts

  • Absolute Value Definition
  • Isolating the Absolute Value
  • Two Possible Solutions

Learning Objectives

  • Students will be able to isolate the absolute value expression in an equation.
  • Students will be able to solve absolute value equations by considering both positive and negative cases.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of absolute value: the distance of a number from zero. Briefly discuss why absolute value equations can have two solutions.
  • Type 1: Absolute Value Already Isolated (15 mins)
    Watch the first part of the video (0:00-4:22). Pause at key points to emphasize the 'blocking out' strategy. Work through the example problems in the video, reiterating the two possible scenarios (positive and negative).
  • Type 2: Absolute Value Not Isolated (15 mins)
    Watch the second part of the video (4:22-end). Emphasize the importance of isolating the absolute value expression *before* splitting the equation into two cases. Work through example problems, highlighting the correct order of operations.
  • Practice and Review (10 mins)
    Students work independently on practice problems involving both types of absolute value equations. Provide support as needed. Review solutions as a class.

Interactive Exercises

  • Equation Challenge
    Divide students into groups. Each group receives a set of absolute value equations of varying difficulty. The first group to correctly solve all equations wins.

Discussion Questions

  • Why does the absolute value of a number always result in a non-negative value?
  • What are the key steps to solving an absolute value equation where the absolute value is not initially isolated?
  • What is the significance of considering both positive and negative cases when solving absolute value equations?

Skills Developed

  • Algebraic Manipulation
  • Problem-Solving
  • Critical Thinking

Multiple Choice Questions

Question 1:

What is the first step in solving an absolute value equation where the absolute value expression is NOT isolated?

Correct Answer: Isolate the absolute value expression.

Question 2:

How many possible solutions can an absolute value equation have?

Correct Answer: Zero, one, or two.

Question 3:

What is the absolute value of -5?

Correct Answer: 5

Question 4:

Which of the following is equivalent to |x| = 3?

Correct Answer: x = 3 or x = -3

Question 5:

Solve for x: |x + 2| = 5

Correct Answer: x = 3 or x = -7

Question 6:

Solve for x: 2|x - 1| = 8

Correct Answer: x = 5 or x = -3

Question 7:

What is the result of taking the absolute value?

Correct Answer: Always non-negative

Question 8:

Which equation has no solution?

Correct Answer: |x| = -2

Question 9:

What is the significance of the 'blocking out' strategy?

Correct Answer: To focus on the two possible values.

Question 10:

Solve for x: |3x| = 9

Correct Answer: x = 3 or x = -3

Fill in the Blank Questions

Question 1:

The absolute value of a number is its ________ from zero.

Correct Answer: distance

Question 2:

Before splitting an absolute value equation into two cases, you must ________ the absolute value expression.

Correct Answer: isolate

Question 3:

The absolute value of -10 is ________.

Correct Answer: 10

Question 4:

An absolute value equation can have zero, one, or ________ solutions.

Correct Answer: two

Question 5:

If |x| = 7, then x = 7 or x = ________.

Correct Answer: -7

Question 6:

The expression inside the absolute value can be either ________ or negative.

Correct Answer: positive

Question 7:

To get rid of multiplication you do the ________ operation, division.

Correct Answer: opposite

Question 8:

If |x+1| = 6, then x = 5 or x = ________.

Correct Answer: -7

Question 9:

Absolute value represents the ________ magnitude of a number.

Correct Answer: non-negative

Question 10:

For an equation like |x| = -5, there are ________ solutions.

Correct Answer: no

Educational Standards

A2.A.1:Represent and solve mathematical and real-world problems using nonlinear equations, systems of linear equations, and systems of linear inequalities; interpret the solutions in the original context. A2.A.2:Generate and evaluate equivalent algebraic expressions and equations using various strategies.

Teaching Materials

Download ready-to-use materials for this lesson:

Student Worksheet Classroom Slides Assessment Quiz Export to Google Docs
Add to Google Classroom

User Actions

Sign in to save this lesson plan to your favorites.

Sign In

Share This Lesson

Related Lesson Plans