The hardest part of answering a question that involves an equation can sometimes be understanding the equation itself. It’s important to understand what each component of an equation is in order to answer questions based on it. If, for example, you don’t know what is meant by a variable, how are you supposed to solve for it? Here I’ll outline the components of an equation so you can avoid confusion when presented with one.
Variable
A variable is typically an unknown quantity written as a letter. X and y are the most common letter choices when it comes to algebraic equations but any letter in the English alphabet, upper or lower case. Often times letters from the Greek alphabet are used as well (more common in science disciplines). A variable will sometimes represent a quantity or have some attached meaning to it where as other times you will have to manipulate variables to prove some form of understanding.
Constant
A constant is exactly what it’s name would lead you to believe. It is a quantity that never changes. The simplest example would be a number. Other times you may be told that a quantity remains “constant” which, as previously stated, means that throughout your problem it will not change.
Term
A term is the product of a constant and a variable. Another way of defining a term would be to say it’s any quantity separated by either addition or subtraction from other quantities. This include a variable with no written constant attached to it as an unwritten constant is just 1. For example, x^2 is consider to be a term as it’s attached constant is 1 (unwritten), provided it it separated from other quantities by either addition or subtraction. Variables with exponents, like in the previous example, can still be part of a term as well as a constant as a constant with no attached variable can be viewed as a constant multiplied by a variable to the exponent 0. An example would be a number such as 4 which can also be written as 4*x^0 as anything to the exponent, or power, 0 is equal to one and omitted in standard text.
Expressions Versus Equations
Expressions are any combination of terms. They can be as simple as a single constant or as complicated as the sum or difference of many different terms. Expressions do not include equal signs and therefore cannot be solved, only simplified. Equations on the other hand are expressions equated or linked by an equal sign. Equations often require the simplification of the expressions in order to solve it but occasionally solutions may be found without any or minimal simplification.
This article was written for you by Troy, one of the tutors with Test Prep Academy.