Math Tutor Bob

Frequently in algebra we will need a symbol to take the place of a number because it is that unknown number which we wish to determine. And since the number is unknown, we need a "place holder" to represent this number. This place holder is frequently called a variable.

For example, we could be given the problem "five times a number is 20, please find the number". We know this is easy to figure out without the use of algebra, but using algebra we might write the following:

    let X = a number  
        ... we are declaring that X will represent a number

    5X = 20 
____________
         

In this instance, X represents a number which we wish to solve for. It is a "place holder" for that number. And "5X" represents 5 times X.

Another thing worth mentioning here is that prior to algebra the "X" was typically used for a multiplication sign. Once we enter algebra, STOP this use of the "X" as it will only confuse you because in algebra the "X" almost always represents the variable, not the multiplication operation.

And one more thing we can discuss relative to 5X = 20 . The "5" is known as the coefficient. And its use in this example means "five times a number which we call X". Also, sometimes a variable (typically X) will have a coefficient which is "invisible". For example consider this equation

         5X+4 = X+20

Don't worry what the answer is (which is X=4), and don't worry how to solve this as that comes later. What you should understand now is that the term "5X" (on the left side of the equal sign) has a coefficient of 5. The term "X" (on the right side of the equal sign) has a coefficient which is invisible and it is one (1). That equation could be rewritten as follows which would mean exactly the same thing.

         5X+4 = 1X+20

The word "term" was used in the previous paragraph. And actually "term" has a mathematical meaning. As wikipedia says,