Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 55,000 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:
*Yuanxin (Amy) Yang Alcocer*

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

In algebra, there are two scenarios that give us interesting results. Watch this video lesson to learn how you can distinguish problems that have no answers and problems that have an infinite number of answers.

When you're solving equations in algebra, it is kind of like a treasure hunt. You are looking for your *x*. You want to know where your *x* is, so you can go find your treasure. With most equations, you will get an answer letting you know where your treasure is located. For example, solving the equation *x* + 3 = 4 by subtracting 3 from both sides gives us *x* = 1 as our answer and location of our treasure.

But sometimes, an equation that you are trying to solve for gives you an answer that just doesn't make sense. It is these types of answers that we are going to discuss in this video lesson. It is important to understand these so you can spot them and identify the equations as unsolvable because they have an answer that doesn't make sense. We will go over the two possible cases where the answer doesn't make sense.

The first is when we have what is called **infinite solutions**. This happens when all numbers are solutions. This situation means that there is no one solution. In terms of our treasure hunt, it means that we can't find the treasure because the location of the treasure can be anywhere. There is no *x* that marks the spot. Our *x* here marks the whole world, which doesn't help us.

The equation 2*x* + 3 = *x* + *x* + 3 is an example of an equation that has an infinite number of solutions. Let's see what happens when we solve it. We first combine our like terms. We see two *x* terms that we can combine to make 2*x*.

2*x* + 3 = 2*x* + 3.

Now we can subtract 3 from both sides: 2*x* = 2*x*. Hmm. This is an interesting situation; both sides are equal to each other. How many different values of *x* will make this equation true? Why, isn't it any number? Yes, and so we have our infinite solutions.

The next case is what is called **no solutions**. In this case, we have no answer. Our problem equation is a dud. In terms of helping us find our treasure, it actually leads us down the wrong path, to a dead end, so to speak. We think we are going somewhere, but in the end, this equation just laughs at us with an end that doesn't make sense.

Let's look at what one of these equations gives us in the end. 3 + 3*x* + 5 = *x* + 2*x* + 9. We first combine like terms. On the left side of the equation, we see a 3 and a 5 that can be combined to get 8, and on the right side we see an *x* and a 2*x* that can be combined to get 3*x*. 3x + 8 = 3x + 9.

Now I can subtract the 3*x* from both sides. I get 8 = 9. Isn't this interesting? It makes no sense because we know that 8 will never equal 9. They are different numbers and will never equal each other. This means that there is no solution.

Let's look at a couple more examples. 9 + *x* = 5 + 4 + *x*. We first combine like terms: 9 + *x* = 9 + *x*. Next, we can subtract 9 from both sides: *x* = *x*. Here we have *x* = *x*. Is there just one value that makes this statement true? No, we can actually have any value for *x*, so this one has infinite solutions.

What about the equation 4*x* + 9 + 1 = 4 + 4 + 2*x* + 2*x*? We combine like terms first: 4*x* + 10 = 8 + 4*x*. Now we subtract 4*x* from both sides: 10 = 8. This doesn't make sense, so we have no solutions.

Now, let's review what we've learned. There are two cases in algebra where our answers won't make sense. The first case is the case of **infinite solutions**, when all numbers are solutions. The next case is **no solutions**, when we have no answer. We can identify which case it is by looking at our results. If we end up with the same term on both sides of the equal sign, such as 4 = 4 or 4*x* = 4*x*, then we have infinite solutions. If we end up with different numbers on either side of the equal sign, as in 4 = 5, then we have no solutions.

Review this lesson to learn how to determine if a mathematical equation has an infinite number of solutions or no solution.

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
16 in chapter 8 of the course:

Back To Course

Algebra I: High School20 chapters | 168 lessons | 1 flashcard set

- What is the Correct Setup to Solve Math Problems?: Writing Arithmetic Expressions 5:50
- Understanding and Evaluating Math Formulas 7:08
- Expressing Relationships as Algebraic Expressions 5:12
- Evaluating Simple Algebraic Expressions 7:27
- Combining Like Terms in Algebraic Expressions 7:04
- Practice Simplifying Algebraic Expressions 8:27
- Negative Signs and Simplifying Algebraic Expressions 9:38
- Writing Equations with Inequalities: Open Sentences and True/False Statements 4:22
- Common Algebraic Equations: Linear, Quadratic, Polynomial, and More 7:28
- Defining, Translating, & Solving One-Step Equations 6:15
- Solving Equations Using the Addition Principle 5:20
- Solving Equations Using the Multiplication Principle 4:03
- Solving Equations Using Both Addition and Multiplication Principles 6:21
- Collecting Like Terms On One Side of an Equation 6:28
- Solving Equations Containing Parentheses 6:50
- Solving Equations with Infinite Solutions or No Solutions 4:45
- How to Solve One-Step Algebra Equations in Word Problems 5:05
- How to Solve Equations with Multiple Steps 5:44
- How to Solve Multi-Step Algebra Equations in Word Problems 6:16
- Algebra Terms Flashcards
- Go to High School Algebra: Algebraic Expressions and Equations

- NES Assessment of Professional Knowledge - Elementary: Test Practice & Study Guide
- GACE School Counseling Test II: Practice & Study Guide
- Business 313: Organizational Communication
- AP Spanish Language and Culture: Exam Prep
- GACE School Counseling Test I: Practice & Study Guide
- Studying for Business 121
- Spanish Verb Tenses
- Discussing Social Issues in Spanish
- Describing People & Places in Spanish
- Understanding Spanish Texts
- Common Core State Standards in Ohio
- Resources for Assessing Export Risks
- Preview Personal Finance
- California School Emergency Planning & Safety Resources
- Popsicle Stick Bridge Lesson Plan
- California Code of Regulations for Schools
- WV Next Generation Standards for Math

- A Comparison of Early River Valley Civilizations
- The Canterville Ghost Chapter 5 Summary
- Richard Parker in Life of Pi: Symbolism, Analysis & Significance
- Similes & Metaphors in Life of Pi: Quotes & Examples
- Performing Basic Operations with Fractions
- Adjective Clauses in Spanish
- Monitoring Portfolio Performance: Techniques & Importance
- Religion in the Neolithic Age
- Quiz & Worksheet - Women in The Iliad
- Quiz & Worksheet - Culture & International Business
- Quiz & Worksheet - Making In-Text Citations
- Quiz & Worksheet - Bunnicula Synopsis
- Imagery: Quiz & Worksheet for Kids
- Growth & Opportunity for Entrepreneurs Flashcards
- Understanding Customers as a New Business Flashcards

- Civics Study Guide
- Prentice Hall Pre-Algebra: Online Textbook Help
- Common Core Math - Statistics & Probability: High School Standards
- English 101: English Literature
- Algebra I: High School
- Holt McDougal Physics Chapter 19: Magnetism
- Settling North America (1497-1732) Lesson Plans
- Quiz & Worksheet - Silent Mutation
- Quiz & Worksheet - Constructions of the Constitution
- Quiz & Worksheet - Directly Proportional
- Quiz & Worksheet - Role & Function of DNA Helicase
- Quiz & Worksheet - Objective Data in Nursing

- Prominent Artists & Works of the 20th Century
- What is Citalopram? - Uses & Side Effects
- Prohibition Lesson Plan
- Treaty of Versailles Lesson Plan
- Descriptive Writing Prompts
- Study.com for Homeschool
- Mock Trial Lesson Plan
- How to Prepare for College
- West Virginia Homeschool Laws
- Multiplication Lesson Plan
- North Carolina Homeschool Laws
- How to Ace a Group Interview

Browse by subject