A basic algebraic equation uses addition, subtraction, division or multiplication with one unknown variable commonly referred to as "x." In these equations, you are given an "x" that works with other numbers and equals something specific. The purpose of these equations is to learn how to solve for "x." This is something you likely do in everyday life without knowing it. If you know how much one thing costs, $3.10, but not a second but you know the total of the two items is $8.20, with subtraction you can determine the cost of the second item. This looks like $3.10 + x = $8.20 in a basic algebraic equation.
Factoring is used to make solving algebraic equations easier. This allows you to pull out like numbers so you can work with the smallest possible numbers when seeking a solution. So if you have something such as 4x + 36 = 40, you can pull out the 4 to work with the lowest numbers possible. This would make the equation 4(x + 9) = 40, to which you can divide both sides by 4, and you are left with x + 9 = 10. This yields x = 1. As problems deal with larger and larger numbers, factoring makes your work much less complex.
All equations with a variable are considered algebraic expressions. As you delve deeper into basic algebra, you will be asked to work with algebraic expressions that do not necessarily have a single answer. Instead of solving for the "x," you are working to combine expressions completely so that when you are given a number for the variable, you can accurately solve the problem. These equations have more than one variable. The equations should be solved for each of the variables so if you were provided with the answer for one variable, you could work out the others. For example, you could recast the equation y = 2x + 2 so that it becomes x = (1/2)y - 1. This expression manipulation is practice for more complicated theories that you will work with as you advance through algebra and calculus.
Formulas are known ways to acquire answers to tangible problems. These can include geometric solutions such as area, perimeter or angle expression. Formulas can help you compare the sizes of things or even convert between different value systems such as inches to centimeters. While these literal equations are not all algebraic at their base, depending on the information you have, you can use algebra to solve for the unknowns in any of the equations. Basic algebra teaches you how to work with varying information to find out what number you are missing in all types of formulas. You can even use algebra to "prove" certain constants such as pi are accurately expressed.