Section 1
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TEACHER: You already know how to use the distributive property. Well, it turns out that we can use the distributive property to help us solve equations. So we're going to be taking a look at how this is done as we continue to answer the question-- how to solve multi-step equations that include parentheses.
Section 2
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TEACHER: Let's take a look at multi-step equations. So an equation in the form a times the quantity x plus b equals c can be solved in two ways. And we'll use this example to show those two ways. So we want to solve 2 times the quantity x plus 3 equals 20 by removing the parentheses using the distributive property. So that means I'm going to take the 2,
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multiply with the x. And take the 2 and multiply with the positive 3. So I end up with 2x plus 6 equals 20. And now I can solve for x. So I subtract 6 from both sides. I get 2x is equal to 14. And now divide both sides by 2. And I find that x is equal to 7.
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Now, what if we were to solve our example using the reciprocal to isolate the parentheses term? Well, let's take a look at that. So here was our original equation. So I'm going to multiply by the reciprocal of 2, which is 1 over 2. So I take 1 over 2 times 2 times the quantity x plus 3 is equal to 1 over 2 times 20.
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Now, on the left-hand side of the equation, 1 over 2 times 2 is going to simplify to just 1, because 2 times 1/2 is 2 over 2, which is just 1. So it essentially cancels out. And I'm left with x plus 3 is equal to 1/2 of 20, which is 10. Now, I'm going to subtract 3 from both sides. The 3's cancel on the left.
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And x is equal to 7. Notice I got the same answer both ways I solved the equation. You could use either method to arrive at the solution to this example.
Section 4
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TEACHER: Let's take a look at this multi-step equation and solve it using the distributive property and the reciprocal to see what kind of solutions we get. So the distributive property first. So let's rewrite 2/3 times the difference 3x minus 21 equals 6. So we use the distributive property, which means I'm going to take this 2/3 and multiply it with the 3x and
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with the negative 21. So I'm going to do 2/3 times 3x minus 2/3 times 21 equals 6. Let's do the multiplication. So 2/3 times 3 is just going to give me a 2x. 2/3 times 21 is going to give me a 14. And that's going to be equal to 6. So now let's continue.
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We're going to add 14 to both sides. It cancels on the left. I g

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