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

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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 it comes to linear equations, there are certain steps you have to take to solve them. One of them is the application of the distributive property when you see a pair of parentheses. Watch this video lesson to learn how.

When it comes to algebra, you will come across **linear equations** very often. What are they? They are equations that, when graphed, give you a straight line. One way you can identify them is to see if any of the variables have exponents attached to them. If none of them do, then you are looking at a linear equation.

For example, 7*x* + 8 = 0 is a linear equation. The equation 5 + 2(*x* + 4) = 1 is also a linear equation. Do you see how both of them have an *x* that is not raised to any power? That is the signature mark of a linear equation; none of the variables will be raised to any power.

Do you see the parentheses in the second equation? This is the type of linear equations that we will be solving in this video lesson. Keep watching and I will show how you can easily solve these equations in a systematic way.

If you need to take a moment to refresh yourself on the basics of solving algebraic equations, such as moving terms from one side of an equation to another and combining like terms, please go ahead and pause this video and do so now.

The mathematical property that we will be applying to our equation is called the **distributive property**. This property tells us that if we see a pair of parentheses being multiplied by a value, then to remove the parentheses, we multiply each term inside of our parentheses with the value outside of the parentheses.

*a*(*b* + *c*) = *ab* + *ac*

As you have noticed in the rest of your algebra lessons, keeping the signs of each term is very important, and we also do the same here. For example, if we have 5(*x* - 2), we remove the parentheses by multiplying our 5 with every term inside of our parentheses.

Yes, we also keep our positive and negative terms the way they need to be. So, removing our parentheses gives us 5*x* - 10. You can think of the parentheses as your arms in a big wannabe group hug.

You want to hug the big group inside the parentheses, but since your arms aren't long enough to reach all the way around, you go around and hug each term by itself. So, our 5(*x* - 2) becomes 5(*x*) - 5(2), which becomes 5*x* - 10.

Now, let's see how we can apply this distributive property to help us solve a linear equation. Let's solve the equation that we began with. 5 + 2(*x* + 4) = 1.

We first see that we can go ahead and move the 5 over to the other side by subtracting it from both sides. Okay. Let's do that.

We get 2(*x* + 4) = -4. Hmm. We can't go any further now because of the parentheses. It's time to apply the distributive property to help us remove the parentheses.

I think of my group hug turning into individual hugs, so I multiply my 2 with the *x*, and then the 4. Doing that, I get 2*x* + 8 = -4. Yay! I've removed the parentheses!

Now, I need to finish up and isolate my *x* to finish solving the problem. I don't have any like terms to combine, so I can go ahead and move the 8 over to the other side now, too. I go ahead and subtract the 8 from both sides to get 2*x* = -12.

Now, I need to divide both sides by 2 to get my *x* by itself. Doing that I get *x* = -6, and I am done. My final answer is -6. Not bad, eh?

What have we learned now? We've learned that to solve **linear equations**, equations that give you a straight line when graphed, we need to use the **distributive property**. This property tells us that if we see a pair of parentheses, to remove the parentheses, we multiply each term inside of our parentheses with the value outside of the parentheses. Once we have done this, we can go ahead and finish up solving our equation by using what we know of moving terms from one side of an equation to another and of combining like terms.

Once you have finished reviewing this lesson you should be able to:

- Identify a linear equation
- Use the distributive property to solve linear equations

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

- What is a Linear Equation? 7:28
- Applying the Distributive Property to Linear Equations 4:18
- Abstract Algebraic Examples and Going from a Graph to a Rule 10:37
- Graphing Undefined Slope, Zero Slope and More 4:23
- Parallel, Perpendicular and Transverse Lines 6:06
- Graphs of Parallel and Perpendicular Lines in Linear Equations 6:07
- How to Write a Linear Equation 8:58
- What is a System of Equations? 8:39
- How Do I Use a System of Equations? 9:47
- Nonlinear Function: Definition & Examples 6:03
- Go to High School Algebra: Linear Equations

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