Title: Solving Absolute Value Equations and Inequalities
Grade Level: 9th10th grade
Objective:  Students will understand the concept of absolute value and its properties.  Students will learn how to solve absolute value equations and inequalities.  Students will apply their knowledge to reallife scenarios involving absolute value.
Materials:  Whiteboard or chalkboard  Markers or chalk  Handouts with practice problems  Graphing calculators (optional)
Procedure:

Introduction (10 minutes) a. Begin the lesson by asking students if they have encountered absolute value before and what they understand about it. b. Define absolute value as the distance a number is from zero on a number line, regardless of its sign. c. Discuss the properties of absolute value, such as a = a and a ≥ 0.

Solving Absolute Value Equations (20 minutes) a. Explain that absolute value equations involve finding the values of a variable that satisfy the equation. b. Start with simple examples, such as x = 5, and guide students through the steps to solve them: i. Set up two equations: x = 5 and x = 5. ii. Solve each equation separately to find the possible solutions. c. Provide more challenging examples, such as 2x  3 = 9, and guide students through the steps to solve them: i. Set up two equations: 2x  3 = 9 and 2x  3 = 9. ii. Solve each equation separately to find the possible solutions. d. Give students handouts with practice problems and allow them to work individually or in pairs to solve them. e. Review the solutions as a class, emphasizing the importance of checking the answers in the original equation.

Solving Absolute Value Inequalities (20 minutes) a. Explain that absolute value inequalities involve finding the range of values that satisfy the inequality. b. Start with simple examples, such as x < 3, and guide students through the steps to solve them: i. Set up two inequalities: x < 3 and x > 3. ii. Graph the solutions on a number line and explain the concept of an open circle for < and >. c. Provide more challenging examples, such as 2x  3 ≥ 5, and guide students through the steps to solve them: i. Set up two inequalities: 2x  3 ≥ 5 and 2x  3 ≤ 5. ii. Solve each inequality separately to find the possible solutions. iii. Graph the solutions on a number line and explain the concept of a closed circle for ≤ and ≥. d. Give students handouts with practice problems and allow them to work individually or in pairs to solve them. e. Review the solutions as a class, emphasizing the importance of shading the correct regions on the number line.

RealLife Applications (10 minutes) a. Discuss reallife scenarios where absolute value equations and inequalities are applicable, such as determining the distance traveled or the time taken. b. Provide examples and encourage students to solve them using the concepts learned in the lesson. c. Discuss the importance of understanding absolute value in various fields, such as physics, engineering, and finance.

Conclusion (5 minutes) a. Recap the main concepts covered in the lesson, including solving absolute value equations and inequalities. b. Address any questions or concerns from students. c. Assign homework that reinforces the concepts learned in the lesson.
Note: Adjust the time allocated for each section based on the pace and needs of your students.
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