2.5 Inequalities

2.5 Inequalities - Inequalities Inequalities Section 2.5...

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Unformatted text preview: Inequalities Inequalities Section 2.5 Interval Notation Interval Let c and d be real numbers with c < d. Let [c, d] denotes the set of all real numbers x denotes such that c < x < d. (c, d) denotes the set of all real numbers x (c, such that c < x < d. [c, d) denotes the set of all real numbers x denotes such that c < x < d. (c, d] denotes the set of all real numbers x denotes such that c < x < d. [ ] represents closed interval. ( ) represents open interval. Basic Principles for Solving Inequalities Inequalities 1. 2. 3. Performing any of the following operations Performing on an inequality produces an equivalent inequality. inequality. Add or subtract the same quantity on both Add sides of the inequality. sides Multiply or divide both sides of the Multiply inequality by the same positive quantity. positive Multiply or divide both sides of the Multiply inequality by the same negative quantity negative and reverse the inequality sign. and Solving Inequalities Solving 1. Write the inequality in one of the following Write forms. f(x) > 0 f(x) > 0 f(x) < 0 f(x) < 0 f(x) f(x) f(x) f(x) 2. Determine the zeros of f, exactly if Determine exactly possible, approximately otherwise. possible, 3. Determine the interval, or intervals, on the Determine x-axis where the graph of f is above (or -axis below) the x-axis. Joke Time Joke Why was the baby cookie Why sad? sad? His mother was a wafer a His while. while. Why couldn’t the elephant Why hide in the cherry tree? hide He forgot to paint his toenails He red. red. ...
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