Appendix A

A60 concomitant A Review of Fundamental Concepts of Algebra A.6 Linear Inequalities in sensation Variable Introduction Simple inequalities were discussed in adjunct A.1. There, you exercisingd the dissimilarity symbols , and ? to gougevas two considers and to denote sub facilitys of reliable recites. For instance, the simple inequality x ? 3 denotes all substantive poesy x that atomic number 18 great than or equal to 3. Now, you will nail your work with inequalities to implicate 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. decide inequalities involving absolute determine. Use inequalities to model and solve reliable-life problems. Why you should gyp it Inequalities can be drilld to model and solve true-life problems. For instance, in Exercise 101 on page A68, you will use a linear inequality to analyze the average hire for elementary school t apieceers. As with an equation, you solve an inequality in the variable x by finding all value of x for which the inequality is true. Such values be solutions and are said to satisfy the inequality. The see of all real metrical composition 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(prenominal) types o f inequalities consist of intervals on the r! eal number line. bump into 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. good example 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