LINEAR INEQUALITY WITH ONE VARIABLE LIOV LEARNING OBJECTIVES

LINEAR INEQUALITY WITH ONE VARIABLE (LIOV)

LEARNING OBJECTIVES: AFTER IMPLEMENTING THIS LESSON STUDENTS WILL BE ABLE TO: 1. 2. 3. 4. � 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.

DEFINITION OF LIOV �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: a) ax + b < 0, for a ≠ 0, b is constant. b) ax + b > 0, for a ≠ 0, b is constant. c) ax + b ≤ 0, for a ≠ 0, b is constant. d) ax + b ≥ 0, for a ≠ 0, b is constant.

THE METHODS TO SOLVING LIOV : 1. 2. 3. 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. o o “>” become “<“ become “≥” become “≤” become “<“ “>” “≤” “≥”

THE SOLUTION SET OF LIOV 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: a) b) c) d) e) f) X=2 X=3 X=4 X=5 X=6 X=7 → → → 2+2>6 3+2>6 4+2>6 5+2>6 6+2>6 7+2>6 ↔ ↔ ↔ 4>6 5>6 6>6 7>6 8>6 9>6 (False) (True)

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

PROBLEM EXAMPLES 1 DETERMINE THE SOLUTION SET OF LIOV BELOW ! (THE SOLUTION SET IS IN INTEGER SET) 1. q 3 x – 4 < 5 Answer: 3 x – 4 + 4 < 5 + 4 (both sides are added by 4) 3 x < 9 x< x<3 -2 -1 0 1 2 3 4 5 6

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

3. q x + 23 ≤ Answer: x+8 x - x + 23 ≤ x- 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, …}

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

EXERCISE 1 DETERMINE THE SOLUTION SET OF LIOV BELOW ! (THE SOLUTION SET IS IN INTEGER SET) 1. 2 a – 3 < a + 5 2. 4 b + 8 ≥ b + 29 3. 4. x+ < - x > 4 x - 1

PROBLEM EXAMPLES 2 DETERMINE THE SOLUTION SET OF LIOV BELOW ! (THE SOLUTION SET IS IN INTEGER SET) 1. q - 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, …}

2. q -4 m > -32 Answer: -4 m > -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}

3. q -8 b + 4 ≥ 18 – 5 b Answer: -8 b + 5 b ≥ 18 – 5 b + 5 b -3 b ≥ 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}

EXERCISE 2 DETERMINE THE SOLUTION SET OF LIOV BELOW ! (THE SOLUTION SET IS IN INTEGER SET) 1. -3 x + < 2. - 3. 11 + 4. 5. d– 3≥ t<5+ t - m < 3 m + 10 - p- < p+