Brief Mathematics (Upper Volume)

Author: Chief Editor: Li Lijuan
Publisher:
Publish Date: 2000-07-01
Features:
Brief Introduction
This set of teaching materials is approximately 170 hours in length. The content arrangement of the teaching materials is basically similar to the original unified textbooks, but it is not a condensation of the original textbooks. The teaching materials emphasize the word "basic," with theorem derivations kept as concise as possible, and calculations focus on introducing methods and patterns. Due to the teaching time constraints, this set of teaching materials has streamlined content such as permutations and combinations, solid geometry, probability, and statistics. The textbooks are divided into two volumes, accompanied by a corresponding exercise book. This book is the first volume, covering topics including inequalities, sets, functions, power functions, exponential functions, logarithmic functions, addition formulas and their corollaries, complex numbers, lines, quadratic curves, and sequences. This set of teaching materials is suitable not only for students in ordinary secondary vocational schools but also for adult secondary vocational schools and technical schools.
Excerpt:
Chapter Inequalities, Sets, and Functions
This chapter is divided into three parts. The first part is the solution of simple inequalities, which is a commonly used basic operation and is widely applied in sets and subsequent content. The second part is sets, which is an important foundation of modern mathematics, and its ideas, methods, and theories are widely used in various fields of mathematics. The third part is functions, which is an important foundation for learning advanced mathematics and other courses, and is also widely applied in practical social contexts.
§1-1 Inequalities
I. Systems of Linear Inequalities in One Variable
1. Definition
A system of linear inequalities in one variable with the same unknown is called a system of linear inequalities in one variable. The common part of the solutions of each inequality in the system is called the solution of the system of inequalities. Examples include all the systems mentioned above.
2. Solving Systems of Linear Inequalities in One Variable
The solutions of a system of two linear inequalities in one variable can be divided into four cases (where \(a\) and \(b\) are real numbers and \(a < b\)), as shown in Table 1-1.
Example 1: Solve the following system of linear inequalities in one variable and represent the solutions on a number line.