Chapter 2: Equations and Inequalities Section 2.2: Solving Inequalities

Section 2.2: Solving Inequalities Goal: Students will be able to solve inequalities and graph the solution sets

Section 2.2: Solving Inequalities Trichotomy Property – For any two real numbers a and b, exactly one of the following statements in true: a < b a = b a > b

Section 2.2: Solving Inequalities Transitive Property For any real numbers a, b and c: If a < b and b < c, then a < c. Example: If 2 < 5 and 5 < 9, Then 2 < 9

Section 2.2: Solving Inequalities Addition Property of Inequality For any real numbers a, b and c: If a > b, then a + c > b + c If a < b, then a + c < b + c Example 3 < 5 3 + (-4) < 5 + (-4) -1 < 1

Section 2.2: Solving Inequalities Subtraction Property of Inequality For any real numbers a, b and c: If a > b, then a – c > b – c If a < b, then a – c < b – c Example 2 > -7 2 – 8 > -7 – 8 -6 > -15

Section 2.2: Solving Inequalities Example 1 Solve 4y – 3 < 5y + 2. Graph the solution set on a number line.

Section 2.2: Solving Inequalities REMEMBER: When multiplying or dividing each side by a NEGATIVE number, you must reverse the inequality symbol

Section 2.2: Solving Inequalities Multiplication Property of Inequality For any real numbers a, b and c where c is positive: If a > b, then ac > bc If a < b, then ac < bc Example -2 < 3 4(-2)< 4(3) -8 < 12

Section 2.2: Solving Inequalities Division Property of Inequality For any real numbers a, b and c where c is positive: If a > b, then a/c > b/c If a < b, then a/c < b/c Example -18 < -9 -18/3< -9/3 -6 < -3

Section 2.2: Solving Inequalities Division Property of Inequality For any real numbers a, b and c where c is negative: If a > b, then a/c < b/c If a < b, then a/c > b/c Example 12 > 8 12/-2 > 8/-2 -6 < -4

Section 2.2: Solving Inequalities The solution set of an inequality can be expressed by using set-builder notation {x | x > 9} The set {} of all numbers x such that (|) x is greater than (>) 9

Section 2.2: Solving Inequalities Example 3 Solve . Graph the solution set on a number line.

Section 2.2: Solving Inequalities Solve and graph 14 – 2x ≤ 4 (6 – x). Write the solution using set builder notation.

Section 2.2: Solving Inequalities Solve and graph 3 (2x – 3) ≥ 5 (x – 3). Write the solution using set builder notation.

Section 2.2: Solving Inequalities Homework: Practice Exercises Pg. 55 #2-32 (even), #37, 38