tailieunhanh - Mathematics - Lecture 9: Inequalities

Mathematics - Lecture 9 "Inequalities" presents the following content: Inequalities: interval notation, order axioms; solving inequalities involving: polynomials and rational expressions, absolute value. | Inequalities Mathematics 17 Institute of Mathematics, University of the Philippines-Diliman Lecture 9 Math 17 (UP-IMath) Inequalities Lec 9 1 / 27 Outline 1 Inequalities Interval Notation Order Axioms 2 Solving Inequalities involving: Polynomials and Rational Expressions Absolute Value Math 17 (UP-IMath) Inequalities Lec 9 2 / 27 Inequalities An inequality is a statement saying that one expression is less than or equal to another. 3x − 2 1 Inequalities Lec 9 3 / 27 Inequalities An absolute inequality is an inequality that is true for all permissible values. Example: x2 + 1 ≥ 2x x 2 1−x≤ x+1 Math 17 (UP-IMath) Inequalities Lec 9 4 / 27 A solution to an inequality is a value of the variable that makes the inequality true. The solution set of an inequality is the set of all solutions of the inequality. Example: The solution set of x2 > x is (−∞, 0) ∪ (1, +∞). Math 17 (UP-IMath) Inequalities Lec 9 5 / .

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