## Chapter 1

## Equations, Inequalities and Basic Logic

#### Learning Objectives

On completing this chapter, you should be able to:

recall some basic ideas related to linear equations, quadratic equations, linear inequalities and quadratic inequalities

solve simple equations and inequalities by the method of drawing graphs

make logically precise statements in some simple and familiar situations

##### 1.1 EQUATIONS AND THEIR SOLUTIONS

*ax* + *b* = 0 (1.1)

is probably the simplest of all mathematical equations. We assume that the constants *a* and *b* are known and try to find the value of *x*, which would satisfy equation (1.1).

Quantities whose values have to be found out from the given equations are called *unknowns*. Equation (1.1) is an example of a linear ...