1-1 - McGraw Hill Education（1 - 1,麦格劳希尔教育）.pdf

2 1 Equations and Inequalities One of the important uses of algebra is the solving of equations and inequalities. In this chapter we look at techniques for solving linear and nonlinear equations and inequalities. In addition, we consider a number of applications that can be solved using these techniques. Additional tech- niques for solving polynomial equations will be discussed in Chapter 3. SECTION 1-1 Linear Equations and Applications • Equations • Solving Linear Equations • A Strategy for Solving Word Problems • Number and Geometric Problems • Rate–Time Problems • Mixture Problems • Some Final Observations on Linear Equations • Equations An algebraic equation is a mathematical statement that relates two algebraic expres- sions involving at least one variable. Some examples of equations with x as the vari- able are 1 x 3x 2 7 1 x x 2 2x2 3x 5 0 x 4 x 1 The replacement set, or domain, for a variable is defined to be the set of numbers that are permitted to replace the variable. Assumpt