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Understanding Linear Equations with One Variable: Definitions, Characteristics, and Solutions

This lesson focuses on Linear Equations with One Variable (LEOV), providing students with essential knowledge and skills. Students will learn to define LEOV, understand its characteristics (such as having an equal sign and one variable), and determine solutions using various methods like addition, subtraction, multiplication, and division. The lesson emphasizes discipline, respect, diligence, and responsibility in mathematics. Through problem examples and exercises, students will apply their understanding to determine the value of variables in LEOV and enhance their problem-solving skills.

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Understanding Linear Equations with One Variable: Definitions, Characteristics, and Solutions

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  1. ASEP BEFI HERMAWAN

  2. LINEAR EQUATION WITH ONE VARIABLE (LEOV)

  3. Learning Objectives:After implementing this lesson students will be able to: • 1. Explaining the definition of linear equation with one variable. • 2. Explaining the characteristics of linear equation with one variable.3. Determining the solution of linear equation with one variable with added, substructed, multiplied and divided method. • The characters building:Discipline, respect, diligence and responsibility.

  4. The Characteristics of LEOV • Have equal sign “=“ • Only have one variable • The power of variable is equal to 1

  5. Determine the forms below, is LEOV or Not LEOV! a + 5 = 7 (LEOV) 2b – 3 = 19 (LEOV) x – 2y = 15 (Not LEOV) 3b + 11 = b (LEOV) X² + 3 = 12 (Not LEOV) 2 + 23 = d (LEOV) 2x = 16 (LEOV) (¼)a – 3 = 10 (LEOV) 3b + b³ = 27 (Not LEOV) 2(x – 1) + 5(2 + x) = 5x (LEOV)

  6. Definition of LEOV • Linear equation with one variable (LEOV) is an open sentence connected by equal sign (“=“) and only have one variable, and the power of variable is equal to 1. • General form of linear equation with one variable (LEOV) is ax + b = 0, for a ≠ 0, b is constant. • Persamaan linier satuvariabeladalahKalimatterbuka yang dihubungkantandasamadengan (“=“) danhanyamempunyaisatuvariabel, danpangkatvariabelnyasamadengan 1. • Bentukumumpersamaan linier satuvariabeladalah ax + b = 0, untuk a ≠ 0, b adalahkonstanta.

  7. The Methods to Solving LEOV: • Both sides are added by the same number. • Both sides are substructed by the same number. • Both sides are multiplied by the same number. • Both sides are divided by the same number.

  8. Problem Examples:(for both sides are added or substructed by the same number methods)Determine the value of variable in LEOV below! • 1. x – 7 = 3 • Answer: x – 7 + 7 = 3 + 7 (both sides are added by 7) x = 10

  9. 2. y + 5 = 12 • Answer: y + 5 – 5 = 12 – 5 (both sides are substructed by 5) y = 7 • 3. 4a – 6 = 3a – 1 • Answer: 4a – 3a – 6 = 3a – 3a – 1 (both sides are substructed by 3a) a – 6 = -1 a – 6 + 6 = - 1 + 6 (both sides are added by 6) a = 5

  10. 4. 3(x - 3) = 2(x + 9) • Answer: 3x - 9 = 2x + 18 3x -2x - 9 = 2x - 2x + 18 (both sides are substructed by 2x) x - 9 + 9 = 18 + 9 (both sides are added by 9) x = 27

  11. Exercise:Determine the value of variable in LEOV below! • x + 7 = 15 • a – 4 = 6 • 5b - 2 = 4b + 9 • 4(x + 5) = 3(x – 6) • 3(2x + 7) + 5(x – 3) = 2(5x + 4)

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