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What is a Variable in Algebra?

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  • 0:07 Variables
  • 1:16 Constants and Coefficients
  • 2:10 Why Use Variables?
  • 3:08 Practice Problems
  • 5:04 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Did you ever encounter something like a + b = c and wonder how all these letters snuck into a math problem? In this lesson, we'll learn about variables, as well as other parts of equations, constants and coefficients.

Variables

Have you ever played poker? Sometimes when I play, I may look at my cards and be one card short of a good hand. Maybe I have three jacks. That's pretty good, but if I just had one more jack, I'd have four of a kind, which is great.

Unfortunately, a deck of cards only has four of each card, so the odds of getting all four jacks in your hand are small. But what if we were playing with wild cards? A wild card is a card that can be whatever you want it to be. It could be a jack for me or an ace for someone else. It's a card that has an undetermined value. This is just like a variable in algebra.

A variable is a symbol that represents an unknown number. It will be equal to a number, but you don't know what that number is yet. Until you figure it out, you use the symbol.

The variable you most often see is x. But a variable can really be any letter or symbol that doesn't otherwise have a number associated with it.

Think again about wild cards. A wild card has something printed on it, but its real meaning is determined by the other cards in your hand. In an algebraic equation, a variable's real meaning is determined by the things around it.

Constants and Coefficients

Before we go any further, let's learn about those other things around our variables. Here's an equation: 2x + 1 = 7.

What are 1 and 7? Numbers! Yes, they're numbers. But we also call them constants. A constant is a fixed quantity that cannot change. It's constant. Constants are our non-wild cards. Just like a 3 of hearts is always a 3 of hearts (supposing that card is never wild), and a 7 is always a 7. By the way, we can't use a number as a variable - since they're constants, that would be too confusing.

Back to our equation, there's also that 2. It has a special name. It's called a coefficient. A coefficient is a number that multiplies a variable. If you have 5y, your coefficient is 5. If you found out that y = 6, then 5y is 5*6, or 30.

Why Use Variables?

You'll often be asked to solve equations with variables, like x - 2 = 5. But you should know that variables don't just exist for algebra quizzes. They have very practical purposes.

Let's say you're at your favorite local burger place. They sell double bacon cheeseburgers for $4 each. You want to get as many as you can, but you only have 13 dollars. Plus, if you're going to buy a bunch of double bacon cheeseburgers, you're also going to need a drink, which costs a dollar. How can you figure out how many burgers you can get? The number of burgers is your variable. Maybe it's 1, maybe it's 7. You don't know. So let's call it x.

Each burger costs $4, so 4x is the cost of a burger times the number of burgers. 4x + 1 is the cost of the burgers and the soda. That has to equal 13, so our equation is 4x + 1 = 13.

You just used a variable to help you solve a crucial problem and help you maximize your double bacon cheeseburger intake.

Practice Problems

But how do you solve this equation? When you're trying to solve an equation that has a variable, you're trying to find out the value of that variable.

Let's first try a simpler example: x - 5 = 10. Our variable is x, so that's what we want to figure out. 5 and 10 are our constants. How do we figure out x? Well, our equation has two parts: x - 5 and 10. They're separated by an equals sign. In order to learn what x is we need to get it alone on one side of the equation. Here, we want to add 5 to both sides. This will get us x = 15. So what is x? It's 15!

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