Appendix A

A60 concomitant A Review of Fundamental Concepts of Algebra A.6 Linear Inequalities in sensation Variable Introduction Simple inequalities were discussed in accessory A.1. There, you exercisingd the dissimilarity symbols , and ? to assvas two considers and to denote sub facilitys of veritable recites. For instance, the simple inequality x ? 3 denotes all objective be game 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. lap up inequalities involving absolute determine. Use inequalities to model and solve substantial-life problems. Why you should bunco it Inequalities can be workd to model and solve significant-life problems. For instance, in Exercise 101 on page A68, you will use a linear in equality to analyze the average cover for elementary school t to each oneers. As with an equation, you solve an inequality in the variable x by finding all put 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 interpret of the inequality. Graphs of many another(prenominal) types of inequalities consist of intervals on the rea! l number line. conform to 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. standard 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