Copyright

Solving Linear Equations with Literal Coefficients

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Solving Linear Equations: Practice Problems

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:07 Literally
  • 0:38 Literal Coefficients
  • 1:30 Solving Literal Equations
  • 3:02 Practice Problems
  • 5:10 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Lesson Transcript
Instructor: Jeff Calareso

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

In this lesson, we'll literally learn about literal coefficients. We'll look at how to solve linear equations that contain literal coefficients and practice solving several problems.

Literally

This lesson is literally the greatest thing you could be watching right now. Literally. Does it bug you when people use 'literally' when they shouldn't? I mean, it's literally the worst thing ever. Well, except for maybe a few things - I don't know, war, climate change, the lack of In-N-Out Burgers where I live. As much as it's literally misused, there are literally good uses of the word 'literal.' And, we're about to literally learn about one in algebra. Literally.

Literal Coefficients

Let's say you're walking down Algebra Street, and you bump into this: ax + 2 = b - 5. Whoa. Hold on. What are you supposed to do with all those letters? And, what kind of street is this where linear equations come to life and wander the streets? That's literally weird.

Your first thought is, 'I gotta move to a new neighborhood. Geometry Street has some cool-looking houses.' But wait, before you pack up, let's look again at this algebraic pedestrian. This equation has literal coefficients. A literal coefficient is a symbol that represents a constant, or a fixed number.

Wait - aren't variables just symbols used to represent numbers? Yes! And, literal coefficients are in many ways similar to variables. But in a linear equation, we treat literal coefficients more like numbers, and we're still trying to solve for the variable.

Solving Literal Equations

Let's look at how this literally works. Remember that stranger from Algebra Street? ax + 2 = b - 5. We just want to solve for x. And, how do we do that? We get x alone on one side of the equation.

First, subtract 2 from both sides. ax = b - 7. If that a were a number, like 7, we'd just divide by that number. We do the same thing with the literal coefficient. If we divide by a, we get x = (b - 7)/a. And, that's our answer. We can't go any further. We're basically defining x in terms of b and a.

When you think about that, since we can't do anything with those literal coefficients, there's actually less math to do. If a and b were numbers in that equation, we'd have to keep solving until we got a final number. This makes literal coefficients literally pretty cool. Note that our literal coefficients here were a and b; we usually use the letters from the beginning of the alphabet for our literal coefficients, like a, b, c, and d.

You may have seen those same letters used as ordinary variables, as in 3a = 15. So, how do we know when we have a variable and when we have a literal coefficient? Literally the easiest way is just to look at what the problem says. Problems with literal coefficients will usually say something like, 'if ax = 15, then x = what?' In this case, by the way, we'd divide both sides by a and get x = 15/a.

Practice Problems

Let's get a little practice. Here's one: 6y - c = b. We want to solve for y. First, we move that c over by adding c to both sides. Then, we just divide both sides by 6 to get y = (b + c)/6.

To unlock this lesson you must be a Study.com Member.
Create your account

Register to view this lesson

Are you a student or a teacher?

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back
What teachers are saying about Study.com
Try it risk-free for 30 days

Earning College Credit

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it risk-free for 30 days!
Create An Account
Support