118 Chapter 1 Linear Equations and Inequalities in One Variable Section 1.4 Linear Inequalities in One Variable Key Concepts A linear inequality is an inequality that can be written in one of the following forms, provided that ax b 6 c ax b 7 c ax b c , , , or Properties of Inequalities 1. If a 6 b, then a c 6 b c. 2. If a 6 b, then a c 6 b c. 3. If c is positive and then and 4. If c is negative and then and a c 7 b c . a 6 b, ac 7 bc a c 6 b c . a 6 b, ac 6 bc ax b c a 0. Examples Example 1 Solve. (Reverse the inequality sign.) (Reverse the inequality sign.) 5x 0 x 6 26 14 x 2 6 3x 14 x 7 6x 7x 7 14 7x 7 6 Set-builder notation: Interval notation: 1, 22 ( 2 x 6 2 14 7 2 a14 x 2 b 7 213x2 Properties 3 and 4 indicate that if we multiply or divide an inequality by a negative value, the direction of the inequality sign must be reversed. Section 1.5 Compound Inequalities Key Concepts is the union of A and B.This is the set of elements A ´ B that belong to set A or set B or both sets A and B. is the intersection of A and B. This is the set of A B elements common to both A and B. Examples Example 1 Union Intersection A A B A B A B B
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