Mastering Absolute Value Inequalities

Algebra 2 Grades High School 30:16 Video
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Lesson Description

Learn how to solve absolute value inequalities with this comprehensive lesson, featuring clear explanations, examples, and problem-solving strategies.

Video Resource

Absolute Value Inequalities Algebra

Kevinmathscience

Duration: 30:16
Watch on YouTube

Key Concepts

  • Absolute Value
  • Inequalities
  • Compound Inequalities
  • Interval Notation
  • Number Lines

Learning Objectives

  • Students will be able to solve absolute value inequalities.
  • Students will be able to represent the solution set of absolute value inequalities on a number line and using interval notation.
  • Students will be able to identify when an absolute value inequality has no solution.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definitions of absolute value and inequalities. Briefly discuss how they are combined in absolute value inequalities. Introduce the video and its learning objectives.
  • Video Viewing (15 mins)
    Play the Kevinmathscience video "Absolute Value Inequalities Algebra." Encourage students to take notes on key concepts and examples.
  • Guided Practice (20 mins)
    Work through examples from the video, pausing to explain each step. Emphasize the process of isolating the absolute value, setting up the compound inequality, and solving for the variable. Discuss the 'A and A' and 'B' interval strategies.
  • Independent Practice (15 mins)
    Provide students with practice problems to solve individually. Circulate to provide support and answer questions.
  • Review and Wrap-up (5 mins)
    Review the key concepts and problem-solving strategies. Answer any remaining questions and assign homework.

Interactive Exercises

  • Number Line Activity
    Provide students with a number line and ask them to graph the solutions to various absolute value inequalities. This can be done on paper or using an online tool.
  • Error Analysis
    Present students with incorrectly solved absolute value inequalities and ask them to identify and correct the errors.

Discussion Questions

  • How does the absolute value of a number affect its position on the number line?
  • Explain the difference between solving absolute value equations and absolute value inequalities.
  • Why do we need to consider two cases when solving absolute value inequalities?
  • How can we determine if an absolute value inequality has no solution?

Skills Developed

  • Problem-solving
  • Analytical Thinking
  • Critical Thinking
  • Algebraic Manipulation
  • Graphing Inequalities

Multiple Choice Questions

Question 1:

What is the first step in solving an absolute value inequality?

Correct Answer: Isolate the absolute value expression

Question 2:

Which of the following represents the absolute value of x?

Correct Answer: |x|

Question 3:

What does |x| < a mean?

Correct Answer: -a < x < a

Question 4:

What does |x| > a mean?

Correct Answer: x < -a or x > a

Question 5:

Solve |x - 2| < 3

Correct Answer: -1 < x < 5

Question 6:

Solve |2x + 1| > 5

Correct Answer: x < -3 or x > 2

Question 7:

What is the solution to |x + 5| = -2?

Correct Answer: No solution

Question 8:

The solution to an absolute value inequality is graphed on a number line. What kind of circle is used to indicate that the value is included in the solution set?

Correct Answer: Closed circle

Question 9:

If the absolute value is less than a negative number, what is the solution?

Correct Answer: No solution

Question 10:

How is a compound inequality represented in interval notation?

Correct Answer: All of the above

Fill in the Blank Questions

Question 1:

The ________ of a number is its distance from zero on the number line.

Correct Answer: absolute value

Question 2:

When solving |x| < a, you rewrite it as a ________ inequality.

Correct Answer: compound

Question 3:

The inequality |x - 3| > 5 means x - 3 < ______ or x - 3 > ______.

Correct Answer: -5, 5

Question 4:

If an absolute value expression is ________ to a negative number, there is no solution.

Correct Answer: equal

Question 5:

The symbol 'U' in interval notation represents the ________ of two sets.

Correct Answer: union

Question 6:

The solution to |x| < 0 is ________.

Correct Answer: no solution

Question 7:

To isolate an absolute value, you perform the ________ operations.

Correct Answer: inverse

Question 8:

A ________ circle on a number line represents that the end point is not included.

Correct Answer: open

Question 9:

When an absolute value has > or < sign, it is called an absolute value ________.

Correct Answer: inequality

Question 10:

The graph of |x| > a consists of two ________ radiating outwards from the center.

Correct Answer: intervals

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.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions.

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