This page is designed to help you better understand how to deal
with basic equations (equations containing only one variable) and
their uses in algebra. Click on any of the links below
to go to that section and start understanding equations!
Equations consisting of fractions (product, quotient, and power)
Quiz on Single Variable Equations
Basic equations (equations containing only one variable, etc.) are usually covered in pre-algebra courses. We've done that on this site as well, so if you want to learn about equations that only deal with whole numbers and one variable, click here.
This section will get you on your way to understanding how to deal with equations that contain variables on both sides of the equals (=) sign, equations that contain fractions and/or decimals, and multiple operations.
To solve complex equations, the one thing to remember is that you need to get the variable isolated before you can solve the equation. When dealing with fractions and decimals, be very careful with your multiplication and division operations!
Throughout your "math experience," you will occasionally see a problem that needs to be solved that is made completely of fractions. While these problems may be intimidating, they are not too hard to solve.
This section will help you understand how to solve this type of equation.
If a = b, then ac = bc when a, b, and c are real numbers.
These equations, which are also called rational equations, are easy to solve when you eliminate the denominator. The multiplicative property of equality, which tells us you can multiply both sides of an equation by the same thing and the equation will still be correct, is used exclusively here.
Quadratic equations are a very complex sort of equation that are easiest to solve by going through a process known as factoring. These equations are second degree polynomial equations. Quadratic equations are so complicated because of the factoring and the fact that they can have 1 or 2 solutions.
This section assumes you know how to factor, and will help you understand quadratic equations.
If pq = 0, then either p or q or both are equal to 0 if p and q are real numbers.
Keeping the Zero Factor Theorem in mind is the key to solving quadratic equations. For example, if you factor the equation x2 + 2x - 15 = 0 you will get (x-3)(x+5) = 0. By the definition of the Zero Factor Theorem, we know that one or both of those factors has to equal zero.
Take the Quiz on single variable equations. (Very useful to review or to see if you've really got this topic down.) Do it!