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Representing a relationship with an equation

In this lesson, we learn about balancing scales and solving equations. We discover that to find a mystery mass, we can set up an equation using equal signs and balance both sides. By subtracting the same amount from each side, we can solve for the unknown mass, helping us understand the relationship between the two sides of the scale. Created by Sal Khan.

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Video transcript

I now want to refigure out what this mystery mass is, but we're going to start using a little bit more of mathematics. And mathematics really are just a language, symbols for representing ideas, for representing relationships between things. And so the first thing I want you to do is think about if you can express a relationship mathematically between this side of the scale and that side of the scale. And I'll give you some hints. We know that they have equal mass. So maybe you can set up some type of relationship using an equal sign, somehow showing that this right over here is equal to that. And I'll give you a few seconds to do that. So let's think about it a little bit. What do we have on this side? Well, we have our mystery mass. And I'll represent that mystery mass by the question mark right over here. But that's not the only thing that we have on the left-hand side. We also have these other 3 kilograms. So let me write over here. We'll assume that we're dealing with kilograms. So we have the mystery mass in kilograms plus 3 more kilograms. That's what we have here on the left-hand side. Now, what do we have here on the right-hand side? Well, we just have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 kilograms. So we just have 10. We just have 10 on the right-hand side. And what else do we know? Well, we know that this scale is balanced, that the mass here is equal to the mass here. Because the scale is balanced the way it's been drawn, we know that these two things are equal. So we have just set up an equation. We're using question mark as our unknown. We don't know what this mystery mass is. If we add 3 kilograms to it, then we see that it has the exact same mass as 10 kilograms. Now my question to you is, what can we do to this equation so that we can essentially solve for the unknown, so that we can figure out what the unknown is? Well, we saw in the last little problem that we had that if we wanted to figure out this mystery mass, we had to remove 3 kilograms from both sides. If we just removed 3 kilograms from one side, then the scale wouldn't be balanced anymore. And we really wouldn't be able to say that the mystery mass is equal to the thing on the right. In order to say they're equal, the stuff has to actually be balanced. So in the last video, we removed 3 of these. We removed 3 kilograms from both sides in order to keep the scale balanced. So mathematically, we'll do the exact same thing over here. We will remove 3, not from one side. If we remove 3 from one side, then it wouldn't be equal anymore. We need to remove 3 from both sides. So we need to remove 3. We need to subtract 3 from both sides of this equation in order to keep the scale balanced. So on the left-hand side, what are we left with? Well, just like over here, we're left with just the question mark. 3 minus 3 is 0. So on the left-hand side, we're left with just the question mark. And on the right-hand side, we're left with 10 minus 3, which is 7. And we get the exact same result. Question mark is equal to 7. And if we're dealing with kilograms, then this is 7 kilograms.