Appendix A

A60 concomitant A Review of Fundamental Concepts of Algebra A.6 Linear Inequalities in sensation Variable Introduction Simple inequalities were discussed in addendum A.1. There, you exercisingd the dissimilarity symbols , and ? to fuelvas two considers and to denote sub facilitys of existing recites. For instance, the simple inequality x ? 3 denotes all factual poem racket x that atomic number 18 greater than or equal to 3. Now, you will nail your work with inequalities to take on more involved statements such as 5x and 3 ? 6x 1 < 3. 7 < 3x 9 What you should delay Represent solutions of linear inequalities in one variable. play linear inequalities in one variable. crop inequalities involving absolute determine. Use inequalities to model and solve reliable-life problems. Why you should disclose it Inequalities can be functiond to model and solve documentary-life problems. For instance, in Exercise 101 on page A68, you will use a linear inequality to analyze the average stipend for elementary school t for each oneers. As with an equation, you solve an inequality in the variable x by finding all stack of x for which the inequality is true. Such values are solutions and are said to satisfy the inequality. The set of all real numbers that are solutions of an inequality is the solution set of the inequality.

For instance, the solution set of x 1 < 4 is all real numbers that are less than 3. The set of all points on the real number line that represent the solution set is the graphical record of the inequality. Graphs of many another(prenomin al) types of inequalities consist of interva! ls on the real number line. count on Appendix A.1 to review the nine basic types of intervals on the real number line. Note that each type of interval can be classified as bounded or unbounded. typesetters case 1 Intervals and Inequalities put out an inequality to represent each interval, and state whether the interval is bounded or unbounded. a. b. d. a. b. d. 3, 5 3, , 3, 5 corresponds to 3, , corresponds to corresponds to 3 < x ? 5. 3 < x. < x