Solution procedures | Worked example

- [Instructor] We're asked, which of the following sequence of steps, when completed, will solve the equation two X minus seven is equal to one for X? So pause this video and see if you can figure it out on your own before we do it together. Okay, so there's two ways that we can approach it. One way, we can look at each of these choices and try to follow their directions and see if it gets us solving for X here. Another way to approach it, which is the way I will approach it to begin with, is to just start with the equation, two X minus seven equals one, and then solve for X, or try to do it in the most efficient way that I can. And this is one of the choices, this is one of the questions where they only want us to pick up one choice, so once we pick one choice, we know that the other ones will not be the correct choice. So if I'm going to solve an algebraic equation like this, the first I try to do is isolate the terms that deal with an X on one side. So to do that, I'd want to get rid of this negative seven. So the best way I can think of doing that is to add seven to both sides, so I'm gonna add seven to the left, and add seven to the right hand side of the equation. Remember, when we're dealing with an equation, if we want the equation to hold true, that the left side is equal to the right side, whatever we do to the left side, we have to do to the right side as well. So if we add seven on the left, we have to add seven on the right. Well, when we do that, our left side is left with just the two X, because you have negative seven plus seven, is equal to the right side, is one plus seven, is equal to eight. Now, how do we solve for X here? Well, we can divide both sides by two, and that will just leave an X on the left hand side. So when we divide both sides by two, we are left with X is equal to eight divided by two, is four. So what are the steps? First, we added seven to both sides, so let me write this down. So first, we added seven to both sides, both sides. And then the second step is, we divided both sides by two. Divided both sides by two. Now, which of these choices match up to that? So here it says divide both sides of the equation by two, then subtract seven from both sides. So this is close, but they're dividing by two first and then, instead of adding seven, they're subtracting. And if you divide by two first, it's not clear that adding or subtracting seven is the right thing to do. We could even try it out with that, if you divided both sides by two first, if you divide the left hand side by two, you would get two X divided by two is X, minus seven over two is equal to 1/2, when you divide the right side by two, and then you subtract seven from both sides, that's definitely not going to solve it for X, we'll rule that out. Divide both sides of the equation by two, then add seven to both sides. So those are the two steps that we just did, but they're in reverse order, so we can rule that one out as well. Subtract seven from both sides of the equation, then multiply both sides by two. No, we added seven to both side of the equation and then we divided both sides by two. Add seven to both sides of the equation, yup that's what we did first, then multiply both sides by two. No, it's going to be then divide both sides by two. Add seven to both sides of the equation, yup, that's what we did first, then divide both sides by two. That's exactly what we did and that will get you solving for X. They were a little bit tricky here, because the last choice here, so we had to work through all of them to find the one that actually worked.