# Solving Equations Using the Distributive Property

Hello! Welcome to this video about solving equations using the distributive property. As a quick refresher, remember, if you have something like this

$$3(5x+9)$$

the distributive property says that you can multiply this first term, the outer term, by every term inside the parentheses. So, if we did this we would get:

$$3\times 5x+3\times 9$$

$$15x+27$$

So, now that we’ve reviewed that, let’s use the distributive property to solve some equations. Let’s take a look at the equation:

$$2(3x-7)+x=21$$

So our first step is to simplify the distributive part. The 2 right here is going to be distributed to the $$3x$$ and to the -7. Notice that it’s not distributed to this $$+x$$ over here. That’s because it’s not inside the parentheses. You only multiply the number outside by each term inside the parentheses; the rest of the part of the equation stays the same.

$$6x-14+x=21$$

So now we can combine like terms on the left side. So $$6x$$ and $$x$$ are like terms.

$$7x-14=21$$

Now we can solve this just like a normal two-step equation. We’ll start by adding 14 to both sides.

$$7x-14+14=21+14$$

$$7x=35$$

And then all we have to do is divide by 7 on both sides.

$$\frac{7x}{7}=\frac{35}{7}$$

$$x=5$$

Let’s look at another problem.

$$5(2x+6)=-2(3x+9)$$

For this one, we have to apply the distributive property to both sides of the equation, so we’re going to start by doing the left side.

$$10x+30=-2(3x+9)$$

Now, our equal sign stays the same and we’re going to apply the distributive property to the right side of the equation.

$$10x+30=-6x-18$$

Now we can solve it like a regular equation. So, we’re going to start by adding $$6x$$ to both sides.

$$10x+6x+30=-6x+6x-18$$

Remember, we want to get all of our $$x$$-terms on one side, and all of our constants on the other side. However you do this is fine; if you wanted to subtract $$10x$$ from both sides and get the $$x$$‘s on the right side instead of the left side, that’s totally fine, it would work as well. This is the way I’m going to work it out though; we’re going to get the $$x$$‘s on the left side and the constants on the right side.

$$16x+30=-18$$

Now, we’re going to subtract 30 from both sides, to move this over to the right side of the equation.

$$16x+30-30=-18-30$$

$$16x=-48$$

And finally, we divide by 16 on both sides.

$$\frac{16x}{16}=\frac{-48}{16}$$
$$x=-3$$