SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS).pptx

GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS). GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)GRADE 10 LESSON IN MATHEMATICS: SOLVE ABSOLUTE VALUE EQUATIONS IN ONE

1. SOLVE ABSOLUTE VALUE EQUATIONS IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)

2. OBJECTIVES The learner will be able to: 1. Review the definition of absolute value. 2. Solve absolute value equations. 3. Solve absolute value inequalities.

3. WHAT IS ABSOLUTE VALUE? Absolute value describes the  distance from zero  that a number is on the number line,   without considering direction. The absolute value of a number is never negative. In general, given any algebraic expression x and any positive number p If |x|=p then x=−p or x=p In other words, the argument of the absolute value x can be either positive or negative p (Use this theorem to solve absolute value equations algebraically.)

4. WHAT IS ABSOLUTE VALUE? Remember: The absolute value is always POSITIVE The absolute value of 5 is 5. The distance from 5 to 0 is 5 units. What is the distance from 0 to 5? What is the distance from 0 to -5? The absolute value of -5 is 5. The distance from -5 to 0 is 5 units.

5. WHAT IS ABSOLUTE VALUE? A IxI = x I3I = 3 I-3I = 3 Ix-2I = 5 I2x-4I = 8 Symbol of Absolute Value: I I B IxI ≤ 3 Ix+2I < 3 Ix+2I ≥ 3 4|x+3|−7 ≤ 5 3+ I4x-5I < 8 Which is the Absolute value of equality and which is the Absolute value of inequality?

6. What is the application of Absolute value in real life? Absolute value is used in various real-life situations to measure distance, calculate differences, and determine magnitude, ensuring that results are always non-negative. This makes it a critical tool in fields ranging from navigation and finance to science and engineering.

7. ABSOLUTE VALUE EQUATION The general form of an absolute value equation: ∣x−a∣=b, where b≥0 To solve this equation, we consider two cases: x−a= b x−a= −b EXAMPLES Solve the equation ∣x−2∣=5 by setting up two equations: x−2=5 ⟹ x=7 x−2=−5 ⟹ x=−3 Therefore, the solution set is x=7 or x=−3

8. ABSOLUTE VALUE EQUATION EXAMPLES: 1.) ∣ 2x−4 ∣ =8 Split the equation into two cases: 2x−4=8 ⟹ x=6 2x−4=−8 ⟹ x=−2 Is the number on the other side of the equation positive? YES Solve both equations 2 x - 4 = 8 2x – 4 = -8 2 x = 12 2x = -4 x = 6 x = -2 Write the solution in various notations: Set Notation: {6,−2} Interval Notation: Since it is a discrete set, it's written as {6,−2}

9. ABSOLUTE VALUE EQUATION EXAMPLES: 2.) ∣x+3∣=0 Split the equation into two cases: x+3=0 ⟹ x=-3 (There is only 1 case since there is no negative or positive 0) Write the solution in various notations: Set Notation: { -3 } Interval Notation: Since it is a discrete set, it's written as { -3 }

10. ABSOLUTE VALUE EQUATION EXAMPLES: 3.) ∣3x+2∣=−5 Split the equation into two cases: ∣3x+2∣=−5 (Since it is -5, t here is no solution to this problem.) Write the solution in various notations: Set Notation: {6,−2} Interval Notation: Since it is a discrete set, it's written as {6,−2}

11. INSTRUCTIONS: Group Assignment: Your group has been assigned an absolute value equation to solve. Work together to find all possible solutions for your equation. Solve the Equation: Solve the given absolute value equation step-by-step. Show your work clearly, including all steps needed to arrive at the solutions. Express Solutions in Different Notations: Once you have the solution(s), express them in the following notations: Standard Notation: Write the solution as individual numbers or expressions (e.g., x=3 or x=−7). Set Notation: Use curly braces to represent the set of solutions (e.g., {3,−7}). Interval Notation: Represent the solution as an interval, if applicable (e.g., (−∞,−2]∪[2,∞). Prepare Your Presentation: Write your final solutions on the provided chart paper. Make sure your work is neat, organized, and large enough for everyone in the class to see. Prepare to explain your reasoning to the class: why you solved the equation in the way you did and how you arrived at your final answers. Present to the Class: One or more group members will present the solution and reasoning to the class. Be ready to answer any questions from your classmates or the teacher about your solution process.

12. Group Activity Group 1: Solve: ∣2x−5∣=7 Express the solution in Standard, Set, and Interval Notations. Group 2: Solve: ∣3x+1∣=4 Express the solution in Standard, Set, and Interval Notations. Group 3: Solve: ∣x−8∣=10 Express the solution in Standard, Set, and Interval Notations. Group 4: Solve: ∣5−2x∣=3 Express the solution in Standard, Set, and Interval Notations. Group 5: Solve: ∣4x−6∣= 12 Express the solution in Standard, Set, and Interval Notations.

13. Group Activity Reflection Questions: What strategies did your group use to solve the equation? How did you decide which notation to use for each solution? Did any challenges arise while solving the equation or presenting it?

14. RECAP • Recap the steps for solving absolute value equations and the importance of considering both cases. • Review how to express solutions in set and interval notations. • Ask a few students to summarize the lesson and share what they found challenging or interesting.

15. WORKSHEET SOLVE ABSOLUTE VALUE EQUATIONS 1. ∣5x+10∣=15 2. ∣2x−3∣=7 3. ∣4x−1∣=0 4. ∣x−1∣=3 5. ∣x−1∣ = 9

16. SOLVE ABSOLUTE VALUE IN EQUALITY IN ONE VARIABLE AND EXPRESS SOLUTIONS IN VARIOUS NOTATIONS)

17. OBJECTIVES The learner will be able to: 1.) Review the definition of absolute value. 2.) Solve absolute value equations. 3.) Solve absolute value inequalities.

18. ABSOLUTE VALUE INEQUALITY An absolute value inequality is an inequality that involves an absolute value algebraic expression with variables. Absolute value inequalities are algebraic expressions with absolute value functions and inequality symbols. That is, an absolute value inequality can be one of the following forms (or) can be converted to one of the following forms: ax + b < c ax + b > c ax + b ≥ c ax + b ≤ c

19. ABSOLUTE VALUE INQUALITY Example: ∣x∣ ≤ 4 This translates to: −4 ≤ x ≤ 4 Interval Notation: [−4,4] represents all values of x between -4 and 4

20. ABSOLUTE VALUE INQUALITY Example: ∣x+2∣ > 3 This translates to two cases: x+2>3 ⟹ x>1 x+2<−3 ⟹ x<−5 Interval Notation: The solution set is: (−∞,−5) ∪ (1,∞)

21. Individual Activity Express the solution in Standard, and Interval Notations 1. I2x-1I > 3 2. I2x-1I < 3 3. I2x-1I ≥ 3 4. I2x-1I ≤ 3 5. I4x-6I < 2