Algebra

Algebra is a branch of mathematics that uses mathematical statements to describe relationships between things that vary overtime. These variables include things like the relationship between supply of an object and its price. When we use a mathematical statement to describe a relationship, we often use letters to represent the quantity that varies, since it is not a fixed amount. These letters and symbols are refferred to as variables. The mathematical statemnets that describes relationships are expressed using algebraic terms, expressions or equations. Before we use algebra to find information about these kinds of relationships, it is important to first cover some basic terminology. Now we will define terms, expressions and equations. Algebraic Terms: The basic unit of an algebraic expression is term. In general, a term is either a number or a product of a number and one or more variables. Here is a term                          -3ax where -3 is a numerical Coefficient and ax is variables. The numerical part of the term, or the number factor of the term, is what we reffer to as the numerical coefficient. The numerical coefficient will take on the sign of the operation in front of it. The term above contains a numerical coefficient, which includes the arithmetic sign, and a variable or variables. In this case the numerical coefficient is -3 and the variables in the term are a and x. Terms such as xz may not appear to have a numerical coefficient, but they do. The numerical cofficients is 1, which is assumed. Algebraic Expressions: An expression is a meaningful collection of numbers, variables and signs, positive or negative, of operaions that must make mathematical and logical sense. Expressions : Contain any number of algebraic terms Use signs of operation - addition, subtraction, multiplication and division. do not contain an equality sign (=) An example of expression is :                                          -3ax + 11wx2y In an expression, the signs of operation separate it into terms. The sign also becomes part of the term that it follows. The expression above contains two terms, the first is -3ax and the second term is 11wx2y. The addition sign separates the two terms. For example, in the expression given above the plus sign (+) separates the -3ax from 11wx2y and is also part of the second term. terms that do not have a sign listed in front of them are understood to be positive. Below are some examples that are not expressions. x + · y  This statement tells us "x plus multiplied by y".This does not make mathematical or logical sense. This collection of symbols is nonsense. y = 2x - 1    This statement is not an expression because expressions are not allowed to contain the equal sign. Algebraic Equations: An equation is a mathematical statement that two expressions are equal. The following three statements are equations:              4 + 5 = 9             x - 35 = 56k2 + 3              x + 3 = 15 The first equation, 4 + 5 = 9, contains only numbers; the other two, however, also contain variables. All three contain two expressions separated by an equal sign : In x - 35 = 56k2 + 3,  x - 35 and  56k2 + 3 both are expressions. When an equation contains variables you will often have to solve for one of those variables.

Absolute Value: The concept of absolute value has many uses, but you probably won't see anything interesting for a few more classes yet. There is a technical definition for absolute value, but you could easily never need it. For now, you should view the absolute value of a number as its distance from zero.