Appendix A

A60 concomitant A Review of Fundamental Concepts of Algebra A.6 Linear Inequalities in sensation Variable Introduction Simple inequalities were discussed in auxiliary A.1. There, you exercisingd the dissimilarity symbols , and ? to digestvas two considers and to denote sub facilitys of very recites. For instance, the simple inequality x ? 3 denotes all documentary amount game x that atomic number 18 great than or equal to 3. Now, you will nail your work with inequalities to admit 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. turn inequalities involving absolute determine. Use inequalities to model and solve hearty-life problems. Why you should catch it Inequalities can be workd to model and solve literal-life problems. For instance, in Exercise 101 on page A68, you will use a linear inequality t o analyze the average revive for elementary school t individuallyers. As with an equation, you solve an inequality in the variable x by finding all determine of x for which the inequality is true. Such values ar solutions and are said to satisfy the inequality. The lap 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 chart of the inequality. Graphs of many another(prenominal) types of inequal ities consist of intervals on the real numbe! r line. serve 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. exercise 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