1.5: Solving Inequalities

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Presentation transcript:

1.5: Solving Inequalities

Key Concepts For any real numbers a, b, and c, if a > b, then: Addition Property: a+c > b+c Subtraction Property: a-c < b-c And if c ≠ 0, Multiplication Property: when c > 0, ac > bc; when c < 0, ac < bc Division Property: when c > 0, (a/c) > (b/c); when c<0, (a/c) < (b/c) And vise versa ( for a < b). Graphing: Open circle means the solution does not include the point; Closed circol means the solution includes the point.

Examples of Simple Inequalities Example Graph

Examples of more complicated multi-step inequalities -4x < (8x + 40)/ 3 -12x < 8x + 40 -20x < 40 x > -2 -7x + 80 < 3x -64 -10x < -144 x > 14.4 Example Graph

Practice Problems x + 2 > 5 x - 7 < -4 8x < 6 128x > 256 Answers: x > 3 x < 3 x < ¾ x > 2 x < 20 x < 4