TABLE OF CONTENTS Solving equations is vital to success in all areas of practical mathematics.We cannot transform shop formulas, analyze geometric relationships, or address the mathematics of the circle and the triangle in trigonometry without this most essential skill.
The word algebra derives from the Arabic words al, meaning the and jabara, meaning reuniting. The parts of an equation are, in a sense, reunited when the equation is solved.
Operations on algebraic expressions and factorization of polynomials are the building blocks of equation solving. Having studied these building blocks in the previous chapters, we now turn to the topic of solving several kinds of equations and inequalities.
The first kind of equation we consider is that of a single variable raised to an exponent of one. These equations may be very simple or less simple. For example:
These are all linear equations in one variable. That is, they represent lines when graphed, as we will later see. These examples by no means represent all types of linear equations. Other linear equations have two variables each raised to an exponent of one. To begin, we will look at linear equations in a single variable.
In general, a linear equation can be written in the form y = ax + b in which a and b represent constants, while x and y are variables.
For most of this chapter we use the letter x to denote the unknown variable. Consider the simplest such equation, that...
