We've been working on solving two step equations. Now we're going to look at an equation that has to be simplified before we can even start solving. So it's almost like a three step equation if you look at it that way. Let's take a look. We have nine x minus five x plus two equals negative ten. A lot going on here. Let's draw our line through the equal sign so we can see each side clearly. Now we can see on the left side that's where a variable x is. But we have two terms that have x with them, the nine x and the five x. We can't start solving this equation quite yet because we have those two terms with x and that's going to be really difficult to work with. So just remember this tip very important. Make sure that each side of the equation is simplified before you start to solve the equation. So we need to simplify that left side first. Remember, when we're simplifying things, we're making it in a shorter, simpler, easier way to work with. And we can do that by combining like terms. So let's combine the nine x and the minus five x that will give us four x. So we can write this whole equation over by simplifying that part to just four x. Now we have four x plus two equals negative ten. This will be much simpler to work with. Now we just need to undo the four and the two so we can isolate the x on that left side. Remember, we're working with the order of operations backwards in reverse. So we undo the addition first. So to undo the plus two, we're going to subtract two and do the same thing on the other side. And now we combine like terms to simplify what we have here, the four X on the left that will stay the same because there's nothing to combine it with. We already simplified in the beginning. Now the plus two and minus two, they'll just equal out to zero, so they cancel each other out. So all I need to do is just bring down the four x. We have an equal sign in the middle that always stays the same. And now on the right side, I can combine like terms with the negative ten and the minus two. Now remember, when we're combining like terms, it's like we're adding these terms together so we can say that we're combining a negative ten and we can treat that as a negative two. Well, negative ten plus negative two gives us negative twelve. Be very careful when you're working with negatives in these equations. Now we just need to undo the four so that we can isolate x. Four is being multiplied by x. So the opposite operation is division. We'll divide by four on the left and divide by four on the right. On the left side, the four over four will cancel each other out because they just simplify to one, it would be one x, which is just x. So they cancel out and I have just x left on the left side, equal sign in the middle and then on the right, negative twelve. Don't forget that negative sign divided by four is a negative three. Now our equation is solved because we have isolated x. We have x by itself on one side of the equal sign and our number, which is our solution by itself on the other side. Now we know that it's important to check our answers, especially with an equation that starts out as complex as this one did. So when we check our answer, we're going to take our original equation, not the one that we simplified, because what if we made a mistake with the simplifying part? So to make sure that our answer is correct, we want to make sure it works in the original equation. So I'm going to take the original equation and substitute negative three for x. And remember, we have two terms with x. So that's two places where we need to substitute that negative three in and it'll look like this. Instead of nine times x, we have nine times negative three. And then our subtraction sign. Instead of five times x, we substituted and got five times negative three. And everything else is the same plus two equals negative ten. Now we need to simplify what we have there to see if all that stuff on the left side is equal to negative ten. So we'll follow the order of operations to simplify this in the correct way. Now we start off with our multiplication. We'll do that before subtraction. In addition, so we need to simplify the nine times negative three and the five times negative three. Nine times negative three becomes negative 27 and the five times negative three becomes negative 15. Now notice I put that negative 15 in parentheses just so that I can notice that negative sign with it. You don't have to do that, but sometimes it's helpful because it just makes that negative sign stand out a little bit more, especially since we have that big old subtraction sign right to the left of it. And then of course, the rest of the equation stays the same. We just copy that down. Now speaking of that negative sign, you notice there we have the subtraction sign and then negative 15. Well, that's two negatives together. Two negatives will become a positive. So we can just make that a little easier to work with by just changing that to a plus sign. So now we have negative 27 plus 15 plus two that needs to be simplified. Now we just need to combine like terms by adding all that stuff together. We'll start with the negative 27 plus 15 that'll become negative twelve. So now we have negative twelve plus two equals negative ten. Add the negative twelve plus two that will equal negative ten. We have negative ten equals negative ten. That's the true equation. So that means our answer was correct, that x does equal negative three for this equation. Okay, so a lot of steps there, but just focus on one step at a time. With problems like this, you want to first make sure that the equation is simplified, that each side of the equation is simplified, and then go through your steps of solving the equation to isolate your variable. And of course, whenever you notice the little negative signs in there somewhere, just take your time and be careful and make sure that you follow the proper rules for working with negatives.