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X Variable: Definition & Concept

Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

In ways, the little x variable is the most popular item in algebra. Learn the many uses of this variable. Also find out why the x variable is not always shown in all algebraic equations and expressions.

What is a Variable?

A variable is used to represent something unknown. In math, you encounter many problems that ask you to find a certain value - like finding the total number of items if there are two piles of the same item. If one pile contains two widgets and the other pile contains five widgets, we can use a variable to represent our total.

The x variable here represents our total.
x variable itself

In some cases, the variable is easy to figure out. In other cases, the variable depends on other variables, too.

The x variable here depends on the variable y.
x variable with y

But, in all cases, the variable stands for an unknown quantity. Sometimes, you can solve it and other times, you can't solve it and would leave it in equation form.

What's So Special About the x Variable?

The x variable seems ubiquitous in math. You see it everywhere. The variable x appears more often than any other variable. Why? This is one of those mathematical things that have always been around and everyone is okay with it. The letter x just seems like a good candidate for it because it stands out as different from any of the numbers. There is the phrase, 'x marks the spot,' that tells you the location of a particular destination. Similarly, in math, the x tells you the location of a point on a graph.

Using the x Variable

The x variable is used in algebra as well as in calculus and higher math. Any math that has unknowns will usually involve the x variable. Using it requires following certain steps that remain the same no matter what level of math you are in.

Step one is that of locating the x variable that you want to solve for. If given a word problem, you will need to define your x variable and set it equal to the item you want to solve for. Say, for example, you get a problem that is asking you to find the area in between two squares - the smaller square being inside the larger square. You are given the areas of the squares. What will you set your x variable equal to? Yes, you will set the x variable equal to the area between the two squares.

Step two is to write down a formula or equation you can use to solve the problem. In our problem with the two squares, think of a way to calculate the area between the two squares. Difference is usually solved by subtraction. So, which area would you subtract from the other? You would subtract the smaller area from the larger area to find the difference.

Step two is setting up the problem and writing an equation.
x variable problem

The A1 is the area of the larger square and A2 is the area of the smaller square. By setting up your problem like this, you have created an equation with your x variable that you can solve.

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