Lesson 4: Solving Inequalities

Recall: Graphing and Writing an Inequality Phrase: “All real numbers less than 2” Set Notation: { x| x < 2, x ε R } 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Recall: Graphing and Writing an Inequality Phrase: “All integers greater-than or equal to -4.” Set Notation: {x|x > -4, x ε I} 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Recall: Graphing and Writing an Inequality Phrase: “All real numbers greater than -3 and less-than or equal to 6.” Set Notation: { x|-3 < x < 6, x ε R} 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Mult/Div Property of inequalities When you multiply or divide an inequality by a negative value, it changes the direction of the inequality.  -x > 4 becomes x < -4

Solve and Graph Ex 1: 5x + 14 < 29 -14 -14 5x ≤ 15 ___ ___ 5 5 Check: Ex 1: 5x + 14 < 29 Pick a value that suits the inequality. For this one, we will use x = 2. 5x + 14 ≤ 29 5(2) + 14 ≤ 29 -14 -14 10 + 14 ≤ 29 5x ≤ 15 ___ ___ 5 5 24 ≤ 29 True! x ≤ 3 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Solve and Graph Ex 2: 25x + 1 < 5x + 41 -5x -5x 20x + 1 < 41 Check: Let’s use x = 0! Ex 2: 25x + 1 < 5x + 41 25x + 1 < 5x + 41 -5x -5x 25(0) + 1 < 5(0) + 41 0 + 1 < 0 + 41 20x + 1 < 41 1 < 41 TRUE! - 1 -1 20x < 40 ___ ___ 20 20 x < 2 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Solve and Graph Ex 3: -11x – 9 < -42 + 9 + 9 -11x < -33 ___ ___ Check: Ex 3: -11x – 9 < -42 -11x – 9 < -42 Let’s use x = 4 + 9 + 9 -11(4) – 9 < -42 -11x < -33 -44 – 9 < -42 What do we do with the symbol when we divide or multiply by a negative? ___ ___ - 11 -11 -53 < -42 TRUE! x > 3 1 2 3 4 5 6 7 -1 -2 -3 -4 -5 -6 -7

Homework: P. 156 #3