Pres Absolute Value Inequalities (Section 1.8)

Rules and Properties ,[object Object],[object Object],1.8 Solving Absolute-Value Equations and Inequalities Absolute-Value Inequalities If a > 0 and | x | < a , then x > – a and x < a . If a > 0 and | x | > a , then x < – a or x > a . Similar statements are true for | x |  a and | x |  a.

Absolute Value Rules ,[object Object],[object Object],[object Object]

Example 1 ,[object Object],| x + 1| = 7 1.8 Solving Absolute-Value Equations and Inequalities

Example 1 ,[object Object],| x + 1| = 7 1.8 Solving Absolute-Value Equations and Inequalities x + 1 = 7 or x + 1 = –7 x = 6 or x = –8

Example 2 ,[object Object],4| x | = 8 1.8 Solving Absolute-Value Equations and Inequalities

Example 2 ,[object Object],4| x | = 8 1.8 Solving Absolute-Value Equations and Inequalities 4 x = 8 or 4 x = –8 x = 2 or x = –2

Example 3 |x - 4| = x + 1 x = x + 5 or x – 4 = -x - 1 0 = 5 or 2x – 4 = -1 x - 4 = x + 1 x - 4 = -(x + 1) No Solution or 2x = 3 No Solution or x = 3/2 3/2

Example 4 ,[object Object],| x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities

Example 4 ,[object Object],| x + 52|  76 x + 52  76 or x + 52  - 76 x  24 or x  – 128 1.8 Solving Absolute-Value Equations and Inequalities

Example 5 ,[object Object],| x + 52|  76 1.8 Solving Absolute-Value Equations and Inequalities

Example 5 ,[object Object],| x + 52|  76 x + 52  76 and x + 52  -76 x  24 and x  –128 1.8 Solving Absolute-Value Equations and Inequalities

Pres Absolute Value Inequalities (Section 1.8)

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