Back To Course

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

Are you a student or a teacher?

Try Study.com, risk-free

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.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

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.

When we have parentheses in our equations it changes the way we solve them. Now we have an added step to do to remove those parentheses. Watch this video lesson to learn how it is done.

What do we do normally when we have parentheses? We usually evaluate the inside of the parentheses first as we follow our order of operations. For example, if we have something like (3 + 1)5 + 2, we should first do the operation inside the parentheses and then evaluate the outside. So, we would do 3 + 1 to get 4 first before multiplying that result by the 5 to get (4)5 = 20. Now we can finish our problem by adding the 2 to get a final answer of 22.

But what if we add a variable into the mix so that we need to solve (3*x* + 1)5 + 2 = 0? What do we do then? We can't add the 3*x* + 1 together. The only way we could combine the 3 and the 1 is if the 3*x* and the 1 were **like terms**, which means that they share the same variable with the same exponents. As you can see, the 3 has an *x* for a variable, but the 1 doesn't. So, what do we do?

In algebra, we have a property to help us remove those parentheses. It's called the **distributive property**, and it tells us that we can remove a pair of parentheses by multiplying the term outside the parentheses with every term inside the parentheses. In the language of algebra, the distributive property looks like this: *a*(*b* + *c*) = *a*(*b*) + *a*(*c*), where *a*, *b*, and *c* are terms, either just numbers or numbers with variables, and the parentheses mean multiplication.

You can see that we've multiplied the term outside with every term inside the parentheses and we've kept the operation inside the parentheses between our multiplications. I like to think of the distributive property as distributing a hug to everybody inside the parentheses. If you think of parentheses as your arms, you can kind of see how it looks like a big hug.

If you have several terms inside the parentheses, it's like giving a group hug to everybody inside. If your arms weren't big enough to give a group hug to everybody, what can you do? You can go around and hug each individual term. Let's see this in action.

We have our equation (3*x* + 1)5 + 2 that we want to solve. We see parentheses with a couple terms inside. I think group hug, but my arms are too short. What do I do? I distribute my hug to each term to get (3*x*)5 + (1)5 + 2. Now I can go ahead and multiply each individual hug to get 15*x* + 5 + 2.

The next step in solving an equation like this is to collect like terms. I take my highlighter and I start by highlighting the 15*x*. I keep going to see if I have any more terms that also have an *x*. I don't see any, so now I choose a different color highlighter. I highlight the next term, the 5. I keep going to see if there are other numbers without variables. I see a 2, so I go ahead and highlight that with the new color. Now I've highlighted all my terms. The 0 I can ignore since the 0 doesn't change anything.

Now I go through and add my like terms. The 15*x* is by itself so there is nothing to add it and it stays the same. The next color highlight has the 5 and a 2, so I can add those together to get 5 + 2 = 7. Now I can rewrite my equation as 15*x* + 7 = 0. I've collected my like terms and I can move on to the next step of solving.

To solve, I need to isolate my variable to get it by itself on one side of the equation. Since the variable is on the left side, I'm going to move everything else to the opposite side. To do this, I first move things that are being added or subtracted. To move things over, I do the opposite of the operation. So if I have addition, I subtract. If I have subtraction, I add. I see that I have an addition of 7, so I will subtract 7 from both sides. Doing this I get 15*x* + 7 - 7 = 0 - 7, which turns into 15*x* = -7.

Now I can move things that are being multiplied and divided. Again, I do the opposite operation. If I see multiplication, I divide. If I see division, I multiply. I see multiplication of 15, so I will divide by 15 on both sides, 15*x* / 15 = -7 / 15. Doing this I get *x* = -7 / 15. This is also my answer since I can't simplify the -7/15 any further. If I had -5/15, then I could simplify it further to get -1/3, and this simplified form would be my answer. But -7/15 can't be simplified any further, so I know that I am done and this is my final answer.

Now, what have we learned? We've learned that to solve an equation involving parentheses, we can use the **distributive property** to help us remove our parentheses. This property tells us we can remove a pair of parentheses by multiplying the term outside the parentheses with every term inside the parentheses.

In algebra language, the distributive property will read as *a*(*b* + *c*) = *a*(*b*) + *a*(*c*). We can think of the distributive property as distributing a big group hug to every individual term inside the parentheses. We also remember that **like terms** are the terms that share the same variable with the same exponents, where terms are either numbers or numbers with variables.

The steps to solve an equation after we remove the parentheses require us to isolate our variable. To do this we start by moving those numbers that are being added or subtracted. I performed the opposite operation to move those numbers over. Next I work on moving those numbers that are being multiplied or divided. Again, I perform the opposite operation to move those numbers over. For every step, I remember that what I do to one side, I have to do to the other. Once my variable is isolated and all my numbers have been simplified, then I am done.

After watching this video lesson and studying its content, you could have the skills necessary to:

- Examine and contrast equations with parentheses with those that have a variable
- Use the distributive property to remove the parentheses
- Understand how to collect and add like terms
- Complete the process of simplifying and solving an equation

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

BackWhat teachers are saying about Study.com

Already registered? Login here for access

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

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
15 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
- Translating Words to Algebraic Expressions 6:31
- 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

- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- U.S. Politics & Civics Lesson Plans
- US History - Civil War: Lesson Plans & Resources
- Computer Science 321: Ethical Hacking
- iOS Data Analysis & Recovery
- Acquiring Data from iOS Devices
- Foundations of Digital Forensics
- Introduction to Mobile Forensics
- Examination of iOS Devices
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison
- TACHS Prep Product Comparison
- Top 50 Blended Learning High Schools
- EPPP Prep Product Comparison
- NMTA Prep Product Comparison
- Study.com NMTA Scholarship: Application Form & Information

- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Logical Thinking & Reasoning Questions: Lesson for Kids
- Amigo Brothers Activities
- Using Graphical Objects in Python
- Tundra Biome Project Ideas
- Quiz & Worksheet - Frontalis Muscle
- Octopus Diet: Quiz & Worksheet for Kids
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Quiz & Worksheet - Dolphin Mating & Reproduction
- Flashcards - Measurement & Experimental Design
- Flashcards - Stars & Celestial Bodies
- 4th Grade Math Worksheets & Printables
- What is STEM Education?

- Conflict Management for Team Leaders
- AFOQT: Practice & Study Guide
- ScienceFusion The Human Body: Online Textbook Help
- Western Civilization I: Help and Review
- Smarter Balanced Assessments - Math Grade 6: Test Prep & Practice
- MTEL Reading Specialist: Analyzing Ideas
- CEOE Physical Science: Matter
- Quiz & Worksheet - Macbeth's Three Apparitions
- Quiz & Worksheet - Angle Pairs
- Quiz & Worksheet - Jane Austen's Persuasion
- Quiz & Worksheet - Maxillary Artery
- Quiz & Worksheet - Promotion Strategies in Marketing

- Elements of a Short Story
- Beah's A Long Way Gone: Summary, Setting & Quotes
- Ohio Science Standards
- Multiple Intelligences Lesson Plan
- Recycling Lesson Plan
- STEM & Next Generation Science Standards
- How Hard is the CSET Multiple Subjects Test?
- ACT Test Scores by State
- Teacher Associations in Texas
- Scientific Method Experiments for Kids
- Illinois TAP Test Registration & Dates
- How to Study for the PSAT

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

Browse by subject