Join Karin Hutchinson for an indepth discussion in this video Solving multistep equations using the distributive property, part of Foundations of Algebra: Solving Equations.
 In this next chapter, you'll be solving equations with the distributive property. Let's start by looking at an equation that contains the distributive property. Here we have three times the quantity, X minus 2, equals 21. You know that you have the distributive property because of the X minus two expression inside a parentheses. Because we have the distributive property we must get rid of the parentheses first. So our very first step for solving this equation is to use the distributive property to remove the parentheses.
Once the parentheses are removed, you may have like terms. If you have like terms, your next step will be to combine those like terms. Once your terms are combined you can then begin solving the equation. Let's take a look at these three steps in action. Our first step is to remove the parentheses by using the distributive property. So I'm going to distribute the three throughout the parentheses. So first I'm going to multiply three times X, which is threeX.
And then, I need to think of this as negative two. So I'm going to multiply three times negative two which is negative six. And that equals 21. So now I have a new equation which is actually a twostep equation that says: threeX minus six equals 21. I do not have any like terms on the lefthand side that can be combined. So I can begin solving. I know that the first number that I need to get rid of is the six because it's the constant in the equation.
So since I'm subtracting six I know that I can add six to both sides of the equation in order to get rid of that six. So I'm going to add six to both sides. And negative six plus six is zero. So I'm left with threeX on the lefthand side equals 21 plus six which is 27. Now I have a onestep equation which is threeX equals 27.
Since I'm multiplying three times X, I can divide both sides by three. Three divided by three is one. So I'm left with just X on the lefthand side and 27 divided by three is nine. So my final answer is X equals nine. Let's take a minute to see if we can check our answer in the original equation. Our original equation was three times the quantity X minus two, and do not forget to put that in parentheses, equals 21.
Now I'm going to substitute my answer, which was nine, for X into the original equation. Now I can begin solving to see if my answer is correct. Since I can subtract nine minus two I don't need to distribute the three. Nine minus two is seven. And three times seven is 21. Since 21 is equal to 21, I know that my answer is correct.
Author
Karin HutchinsonReleased
10/19/2015 Isolating variables
 Keeping equations balanced
 Solving addition and subtraction equations
 Solving multiplication and division equations
 Solving equations that involve the distributive property
 Solving twostep and multistep equations
 Solving equations with decimals and fractions
 Solving equations with variables on both sides
 Understanding literal equations
 Solving absolute value equations
Skill Level Appropriate for all
Duration
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Introduction

Welcome1m 4s


1. Introduction to Solving Equations

Keeping equations balanced1m 30s

2. Addition Equations

3. Subtraction Equations

4. Multiplication Equations

5. Division Equations

6. TwoStep Equations

Solving a twostep equation1m 56s

7. Solving Multistep Equations with the Distributive Property

8. Solving Equations with Decimals

9. Solving Equations with Fractions

10. Solving Literal Equations

11. Equations with Variables on Both Sides

12. Solving Multistep Equations

13. Solving Absolute Value Equations

Conclusion

Next steps37s

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Video: Solving multistep equations using the distributive property