


Algebra I

Algebra is the language through which we describe patterns. Think of it as a shorthand, of sorts. As opposed to having to do something over and over again, algebra gives you a simple way to express that repetitive process. It's also seen as a "gatekeeper" subject. Once you achieve an understanding of algebra, the higher-level math subjects become accessible to you. Without it, it's impossible to move forward. It's used by people with lots of different jobs, like carpentry, engineering, and fashion design. In these tutorials, we'll cover a lot of ground. Some of the topics include linear equations, linear inequalities, linear functions, systems of equations, factoring expressions, quadratic expressions, exponents, functions, and ratios.
Community Questions
Linear equations
We will now equate two algebraic expressions and think about how it might constrain what value the variables can take on. The algebraic manipulation you learn here really is the heart of algebra.
All content in “Linear equations”

The why of algebra

Algebra seems mysterious to me. I really don't "get" what an equation represents. Why do we do the same thing to both sides? This tutorial is a conceptual journey through the basics of algebra. It is made for someone just beginning their algebra adventure. But even folks who feel pretty good that they know how to manipulate equations might pick up a new intuition or two.

Super Yoga plans

This tutorial is a survey of the major themes in basic algebra in five videos! From basic equations to graphing to systems, it has it all. Great for someone looking for a gentle, but broad understanding of the use of algebra. Also great for anyone unsure of which gym plan they should pick!

Equations for beginners

Like the "Why of algebra" and "Super Yoga plans" tutorials, we'll introduce you to the most fundamental ideas of what equations mean and how to solve them. We'll then do a bunch of examples to make sure you're comfortable with things like 3x – 7 = 8. So relax, grab a cup of hot chocolate, and be on your way to becoming an algebra rockstar. And, by the way, in any of the "example" videos, try to solve the problem on your own before seeing how Sal does it. It makes the learning better!

Linear equation word problems

Now that we are reasonably familiar with what a linear equation is and how we can solve them, let's apply these skills to tackling real-world problems.

More fancy equations for beginners

You've been through "Equation examples for beginners" and are feeling good. Well, this tutorial continues that journey by addressing equations that are just a bit more fancy. By the end of this tutorial, you really will have some of the core algebraic tools in your toolkit!

Solutions to linear equations

Not every linear equation has exactly one solution. Some have no solutions and others might have an infinite number of solutions. This tutorial will give you the intuition on when these different situations arise.

Solving for a variable

You feel comfortable solving for an unknown. But life is all about stepping outside of your comfort zone--it's the only way you can grow! This tutorial takes solving equations to another level by making things a little more abstract. You will now solve for a variable, but it will be in terms of other variables. Don't worry, we think you'll find it quite therapeutic once you get the hang of it.

Converting repeating decimals to fractions

You know that converting a fraction into a decimal can sometimes result in a repeating decimal. For example: 2/3 = 0.666666..., and 1/7 = 0.142857142857... But how do you convert a repeating decimal into a fraction? As we'll see in this tutorial, a little bit of algebra magic can do the trick!

Age word problems

In 72 years, Sal will be 3 times as old as he is today (although he might not be... um... capable of doing much). How old is Sal today? These classic questions have plagued philosophers through the ages. Actually, they haven't. But they have plagued algebra students! Even though few people ask questions like this in the real-world, these are strangely enjoyable problems.

Simplifying complicated equations

You feel good about your rapidly developing equation-solving ability. Now you're ready to fully flex your brain. In this tutorial, we'll explore equations that don't look so simple at first, but that, with a bit of skill, we can turn into equations that don't cause any stress! Have fun!

Evaluating expressions with unknown variables

When solving equations, there is a natural hunger to figure out what an unknown is equal to. This is especially the case if we want to evaluate an expression that the unknown is part of. This tutorial exposes us to a class of solvable problems that challenges this hunger and forces us to be the thinking human beings that we are! In case you're curious, these types of problems are known to show up on standardized exams to see if you are really a thinking human (as opposed to a robot possum).

Old school equations with Sal

Some of Sal's oldest (and roughest) videos on algebra. Great tutorial if you want to see what Khan Academy was like around 2006. You might also like it if you feel like Sal has lost his magic now that he doesn't use the cheapest possible equipment to make the videos.