Number systems provide the basic steps to working on intermediate algebra problems. Natural numbers are a set of numbers 1, 2, 3... that continue to infinity. Prime numbers are numbers that can only be divided into a whole number by 1 and itself. Composite numbers are numbers that are not prime numbers. Whole numbers are a set of natural numbers plus zero. Integers are a set of whole numbers but also extend into the negative infinity. Rational numbers are fractions where the denominator and numerator are integers but the denominator is not zero.
The goal of equations in algebra are to solve for "x," and in intermediate algebra there are many difficult expressions you have to work through. To aid in this, there are a two properties to equations you learn. These properties provide the basic steps to solving intermediate algebra equations. If "a=b," the first property states that "a+/-c =b+/-c." The second property states that "ac=bc" and "a/c=b/c."
Students in intermediate algebra will need to move beyond basic math and approach logic. Compound inequalities are the basic steps to approaching logic in intermediate algebra. You need to know how the simple words "and" and "or" work in compound expressions. If you have "3-2x<-1 and 3-2x>1" then you solve for each expression independently and write the answer as the combination of both answers; for example, "2<x<1." If you have "3-2x<-1 or 3-2x>1," then the answer would be to indicate x is one answer or the other "( x>2 or x<1)."
In intermediate algebra, you will encounter many different types of advanced functions, such as linear, absolute value, quadratic, polynomial, rational, exponential and logarithmic functions. For this reason, the basic step to approaching functions is to understand what they are. Functions are relations where each object in the domain is paired with only one object in the range. This basically means a function is a relation where on an "x" and "y" plane, every "x" has a "y."