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Applying the Distributive Property to Linear Equations

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  • 0:02 Linear Equations
  • 1:12 Distributive Property
  • 2:24 Applying the Property
  • 3:14 Steps to Solve
  • 3:43 Lesson Summary
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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.

Linear Equations

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, 7x + 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 Distributive Property

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 5x - 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 5x - 10.

Applying the Distributive Property

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.

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