Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

Are you a student or a teacher?

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Jeff Calareso*

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

With practice, linear equations can be straightforward to solve. In this lesson, we'll define linear equations and learn how to solve them. We'll look at multiple practice problems and walk through solving each one.

*X*. *X* is everywhere. It's the checkbox on the user agreement we never read. It marks railroad crossings and superhero uniforms. And, it's at the end of every pirate map. In all these examples, *x* stands for something. For example, on that pirate map, *x* is where you'll find the buried treasure. In algebra, *x* is sort of like a marker for treasure, if by treasure we mean a number. That's because *x* is a common variable. And, a **variable** is a symbol used to represent a number.

Here we're going to solve for *x* in linear equations. It's just like following a pirate map, where we follow the clues until we know where *x* is. Fortunately, with linear equation solving, you're much less likely to lose a leg or an eye. And, scurvy is very rare. First, let's do a quick review of what these equations are.

A **linear equation** is simply an algebraic expression that represents a line. These equations commonly contain one or two variables, usually *x* or *y*. These are called first-degree equations because the variable's exponent is always one.

We won't see anything like *x*^2 or *x*^3. Those may get you lines like what you'd actually see on a pirate map. But, our pirate map has straight lines. It's much easier that way. You also won't see things like *x* times *y*, *x* over *y* or the square root of *x*. That's for pirates who travel through time and space.

Oh, and the linear equations we'll be solving here only have one variable, not two or more. I mean, if we had both *x* and *y*, how do we know which one has the treasure and which one is a trap? Pirates are big into traps.

As I mentioned before, to solve one of these equations, we're trying to solve for *x*. If you have *x* - 4 = 10, then 10 isn't where the treasure is. It's where *x* - 4 is. And, that's just not what we need.

To solve this equation, we need to get *x* alone on one side of the equation. Here, we do that by adding 4 to each side. That gets us *x* = 14. So, that's our treasure. I know that's a modest haul, but it was a basic equation.

For all of these equations, we'll always just do whatever we can to isolate *x*. If we have 2*x* = 6, we divide by 2 to get *x* = 3. Just keep your focus on *x*.

Now that we know what to do, let's go after some serious treasure. Let's start with *x* + 2 = 9. This looks like the first one we saw. This is like Pirate Treasure Hunting 101. Let's subtract 2 from both sides to get *x* = 7. It's another small treasure, but it is ours.

What about 3*x* - 4 = 11? Let's add 4 to each side. Then divide by 3. We get *x* = 5. That's a little more gold. We could buy ourselves a parrot.

Here's another: 4*x* - 9 = 2*x* - 3. We have *x*s on both sides, so we need to move them around. Let's subtract 2*x* from both sides. Now add 9 to both sides. Then divide by 2. That's *x* = 3. I think we can get a pretty sweet sword with that.

Okay, now let's try *x*/4 + 2 = 5. First, subtract 2 from both sides. And, how do we get rid of that 4? We multiply both sides by 4. So, *x* = 12. Maybe we should put some of this gold in our Pirate College Fund. You know, pirates don't do that well in school. They're always in the high Cs.

Okay, that was bad. Let's go after more treasure. What about 2(*x* + 4) = 22? We first need to distribute that 2 across the *x* + 4. We get 2*x* + 8. Next, subtract 8 from both sides. Then divide by 2. So, *x* = 7. Maybe we can buy a better pirate joke book with that.

Here's one: 6*x* - 1 - *x* = 26 - 4*x*. Let's combine all those *x*s. 6*x* - *x* is 5*x*. Then we add 4*x* to both sides to get 9*x* over here:

Add 1 to both sides to get 9*x* = 27. Divide by 9, and *x* = 3. Now we're getting some gold.

Let's try a tougher one: 3*x*/4 + 2/3 = 5/6 + *x*. Oh, man. What do we do here? We need the lowest common multiple of 4, 3 and 6. That's 12. So, we multiply both sides by 12. That gets us 12(3*x*/4) + 12(2/3) = 12(5/6) + 12(*x*). That last one is just 12*x*. What about the others? 12(3*x*/4) is 36*x*/4. That reduces to 9*x*. 12(2/3) is 24/3, which is 8. And 12(5/6) is 60/6, or 10. Okay, 9*x* + 8 = 10 + 12*x*. Let's subtract 12*x* from both sides to get -3*x* over here:

Then subtract 8 from both sides to get 2 over here:

Finally, divide by -3. So, *x* = -2/3. Now that's a treasure. We could buy our very own pirate ship with that.

In summary, being a pirate is all about finding the right parrot. Wait, no. That's not what we learned here. We learned about solving linear equations. A **linear equation** is an algebraic expression that represents a line. We focused on single **variable** equations, where we try to get *x* alone on one side of the equation. Once we find *x*, we have our treasure!

You should be able to solve linear equations with a single variable after watching this video lesson.

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

Create your account

Are you a student or a teacher?

Already a member? Log In

BackDid 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

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.

You are viewing lesson
Lesson
5 in chapter 8 of the course:

Back To Course

ELM: CSU Math Study Guide17 chapters | 147 lessons | 7 flashcard sets

- What is a Linear Equation? 7:28
- How to Write a Linear Equation 8:58
- Problem solving using Linear Equations 6:40
- Solving Linear Equations with Literal Coefficients 5:40
- Solving Linear Equations: Practice Problems 5:49
- How Do I Use a System of Equations? 9:47
- Solving a System of Equations with Two Unknowns 6:15
- Solving Problems Involving Systems of Equations 8:07
- What is an Inequality? 7:09
- Solving Linear Inequalities: Practice Problems 6:37
- Go to ELM Test - Algebra: Linear Equations & Inequalities

- GRE Information Guide
- Computer Science 310: Current Trends in Computer Science & IT
- Earth Science 105: Introduction to Oceanography
- Computer Science 331: Cybersecurity Risk Analysis Management
- Computer Science 336: Network Forensics
- Practical Applications for Excel
- Practical Applications in Business Law
- Practical Applications for How to Network
- Practical Application for Technical Writing
- Practical Applications for Workplace Communications with Computers
- MEGA Test Accomodations
- Study.com Grant for Teachers
- What are the MEGA Tests?
- MOGEA Test Score Information
- ASWB Prep Product Comparison
- What is the MOGEA Test?
- TASC Exam Registration Information

- Promoting Motor Learning With Activities, Sports & Games
- How to Teach Conflict Resolution to Kids
- Witchcraft in the Jacobean Era
- Best Practices for Teaching Gifted Students
- Practical Application: Principles of Composition in Graphic Design Infographic
- Recursion & Recursive Algorithms in Python: Definition & Examples
- Practical Application: Five Major Consumer Rights Infographic
- Food & Beverage Service & Operations: Assignment 2 - Research Paper
- Quiz & Worksheet - Aristotelian Virtue Ethics
- Quiz & Worksheet - Assessing Diverse Learners
- Quiz & Worksheet - Citizen Journalism Overview
- Quiz & Worksheet - Neolithic Period Overview
- Quiz & Worksheet - When to Intercede in Conflict as a Manager
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies

- Middle School Earth Science: Tutoring Solution
- Precalculus: Homework Help Resource
- Math 102: College Mathematics
- How to Choose a Major: Guidance Counseling
- History 102: Western Civilization II
- Math Foundations
- SAT Reading - US Documents & Speeches: Tutoring Solution
- Quiz & Worksheet - Purpose of Informed Consent in Research
- Quiz & Worksheet - Existing Statistics to Collecting Social Research Data with Existing Statistics
- Quiz & Worksheet - Causes of Earthquakes
- Quiz & Worksheet - Items within a Merchandise Inventory
- Quiz & Worksheet - Requirements of External Validity

- Fruit Fly Behavior: Biology Lab
- Homeland Security Advisory System: Colors & History
- Dr. Seuss Quotes
- Homeschooling in Texas
- Plant Cell Project Ideas
- Professional Resources for Studying Medicine
- New Jersey Science Standards for First Grade
- Teacher Associations in Texas
- Homeschooling in New York
- Earth Day Poster Ideas
- Homeschooling in Delaware
- Study.com's Bachelor's Degree in Business: Degree Plan

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject