Why we do the same thing to both sides of an equation
We've got a scale here, and as you see, the scale is balanced. And we have a question to answer. We have this mystery mass over here. It's a big question mark on this blue mass right over here. And we also have a bunch of 1-- I guess we could call them 1-kilogram masses. So these are all each a 1-kilogram mass. And my question to you is, what could we do to either side of this scale in order to figure out what the mystery mass is? Or maybe we can't figure it out at all. Is there something that we can do, either removing or adding these things, so that we can figure out what this mystery mass is? And I'll give you a couple of seconds to think about that. Well, to figure out what this mystery mass is, we essentially just want this on one side of this scale. But that by itself isn't enough. We could just remove these 3, but that won't do the job, because if we just remove these 3, then the left-hand side of the scale is clearly going to have less mass, and it's going to go up, and the right side is going to go down. And that's not going to give as much information. It's just going to tell us that this blue thing has a lower mass than what's over here. So just removing this won't help us much. It won't let us know that this is equal to that. Well, what we've got to do if we want to keep the scale balanced is we've got to remove the same amount of mass from both sides of the scale. So if we want to remove 3 things here-- so let me try my best to remove 3 things here. If we want to remove 3-- let me do it like this. I'll just color on it. I'll just erase it. So if we want to remove 3 things there, if we did this by itself, just removed these 3 things, then the two sides would not have an equal mass anymore. This side over here would have a lower mass. So we've got to remove 3 from both sides. So if we really want to make sure that our scale is balanced, we've got to remove 3 from both sides. And so if we started off with the scales balanced and then we removed 3 from both sides, the scale will still be balanced. And then when we do that, we have a clearer idea of what the mass of this object actually is. Now, when we remove 3 from both sides, the scale will still be balanced. And we know that this mass is equal to whatever's left over here. It's equal to 1, 2, 3, 4, 5, 6, 7. And if we're assuming they're kilograms, we'll know that the question mark mass is equal to 7 kilograms, that this right over here is a 7-kilogram mass.