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LINEAR INEQUALITY WITH ONE VARIABLE (LIOV)

LINEAR INEQUALITY WITH ONE VARIABLE (LIOV). Explaining the definition of inequality. Explaining the definition of Linear Inequality with One Variable (LIOV). Explaining the characteristics of Linear Equation with One Variable (LIOV).

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LINEAR INEQUALITY WITH ONE VARIABLE (LIOV)

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  1. LINEAR INEQUALITY WITH ONE VARIABLE (LIOV)

  2. Explaining the definition of inequality. • Explaining the definition of Linear Inequality with One Variable (LIOV). • Explaining the characteristics of Linear Equation with One Variable (LIOV). • Determining the solution set of Linear Inequality with One Variable with added, substructed, multiplied and divided method. • The characters building:Discipline, respect, diligence and responsibility. Learning Objectives:After implementing this lesson students will be able to:

  3. Linear Inequality with One Variable (LIOV) is an open sentence connected by inequality signs (<, >, ≤ or ≥) and only have one variable, and the power of variable is equal to 1. • General form of linear equation with one variable (LIOV) is: • ax + b < 0, for a ≠ 0, b is constant. • ax + b > 0, for a ≠ 0, b is constant. • ax + b ≤ 0, for a ≠ 0, b is constant. • ax + b ≥ 0, for a ≠ 0, b is constant. Definition of LIOV

  4. Adding or substracting both sides by the same number without changing the sign of inequality. • Multiplying or dividing both sides by the same positive number without changing the sign of inequality. • Multiplying or dividing both sides by the same negative number, but the sign of inequality is changed. • “>” become “<“ • “<“ become “>” • “≥” become “≤” • “≤” become “≥” The Methods to Solving LiOV :

  5. Example: Determine the solution set (integer number) of this LIOV! x + 2 > 6 To understanding the solution of LIOV above, determine the truth value of statements below! Let: X = 2 → 2 + 2 > 6 ↔ 4 > 6(False) X = 3 → 3 + 2 > 6 ↔ 5 > 6(False) X = 4 → 4 + 2 > 6 ↔ 6 > 6(False) X = 5 → 5 + 2 > 6 ↔ 7 > 6(True) X = 6 → 6 + 2 > 6 ↔ 8 > 6(True) X = 7 → 7 + 2 > 6 ↔ 9 > 6(True) X = 8 → 8 + 2 > 6 ↔ 10 > 6(True) The solution set of liov

  6. So, the solution set of LIOV above is {5, 6, 7, 8, …} That solution set can imaged by the line of number below ! 0 1 2 3 4 5 6 7 8

  7. 3x – 4 < 5 • Answer: 3x – 4 + 4 < 5 + 4 (both sides are added by 4) 3x < 9 x < x < 3 -2 -1 0 1 2 3 4 5 6 The solution set of this LIOV is {…, -2, -1, 0, 1, 2} PROBLEM EXAMPLES 1Determine the Solution Set of LIOV Below !(The solution set is in integer set)

  8. 2. 6x – > 5x + • Answer: 6x - + > 5x + + 6x > 5x + 6x > 5x + 2 6x – 5x > 5x - 5x + 2 x > 2 -2 -1 0 1 2 3 4 5 6 The solution set of this LIOV is {3, 4, 5, …}

  9. x + 23 ≤ x + 8 • Answer: x - x + 23 ≤ x - x + 8 23 ≤ x + 8 23 ≤ x + 8 23 - 8 ≤ x + 8 – 8 15 ≤ x x ≥ 15 11 12 13 14 15 16 17 18 19 The solution set of this LIOV is {15, 16, 17, 18, 19, …}

  10. 3x + ≥ • Answer: 3x + ≥ - x 3x + x + ≥ - x + x x + ≥ x + - ≥ - x ≥ x . ≥ . ↔ x ≥ ↔ x ≥

  11. x ≥ -3 -2 -1 0 1 2 3 4 5 The solution set of this LIOV is {1, 2, 3, 4, 5, …}

  12. 2a – 3 < a + 5 4b + 8 ≥ b + 29 x + < - x > 4x - 1 EXERCISE 1Determine the Solution Set of LIOV Below !(The solution set is in integer set)

  13. - y ≤ 3 • Answer: - y (-2) ≤ 3 (-2) y ≥ -6 -10 -9 -8 -7 -6 -5 -4 -3 -2 The solution set of this LIOV is {-6, -5, -4, -3, -2, …} PROBLEM EXAMPLES 2Determine the Solution Set of LIOV Below !(The solution set is in integer set)

  14. -4m > -32 • Answer: -4m > -32 -4 -4 m < 8 3 4 5 6 7 8 9 10 11 The solution set of this LIOV is {…, 3, 4, 5, 6, 7}

  15. -8b + 4 ≥ 18 – 5b • Answer: -8b + 5b ≥ 18 – 5b + 5b -3b ≥ 18 -3b ≥ 18 -3 -3 b ≤ -6 -10 -9 -8 -7 -6 -5 -4 -3 -2 The solution set of this LIOV is {…, -10, -9, -8, -7, -6}

  16. -3x + < - d – 3 ≥ 11 + t < 5 + t - m < 3m + 10 - p - < p + EXERCISE 2Determine the Solution Set of LIOV Below !(The solution set is in integer set)

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