I have to multiply the right-hand side by one-third. So what if I were to multiply the left-hand side by one-third - but if I want to keep the scale balanced, Now, this turns into a problem very similar to what we saw in the last video, so now I ask you: what can we do to isolate one x, to only have one 'X' on the left-hand side of the scale, while keeping the scale balanced? The easiest way to think about it is: If I want one X on this left-hand side, that is a third of the total X's here. Since we removed the same amount from both sides, our scale is still balanced. And you see that there, the ones that I have not crossed out, there are 12 left, and here you have 3 of those X-blocks. We are subtracting 2 from this side, So on the left-hand side we now haveģx + 2, minus 2 we are left with just 3x, and on the right-hand side we had 14 and we took away 2 (let me write this:) we took away 2, so we are going to be left with 12 blocks.
We are subtracting 2 kilograms from each side. So, we can remove two there,Īnd then we can remove two over there. We need to remove 2 from the right-hand side. So, if we remove 2 block from the left-hand side, But we want to keep it balanced so we can keep saying 'equal'. Now the left-hand side will be lighter and it will move up. Well, the simplest thing is: you can take these 1kg blocks off of the left-hand side, but remember, if you just took these blocks off of the left-hand side, and it was balanced before, Let us think about a few things: how would you first go about at least getting rid of these little 1kg blocks? I will give you a second to think about that. I do not like that brown) Now, what I want you to think about, and you can think about it either through the symbols or through the scales, is: how would you go about. So this mass over here must be equal to this total mass. And we see that the scale is balanced, not tilting down or upwards. We can simply count them: Fourteen blocks, each has a mass of 1 kg, Now, let us think about what we have on the right-hand side. That is what we have on the left-hand side. So one way to think about the total mass on the left-hand side is 3x + 2. We have 3x and then we have 2 masses of 1 kilogram, So let's think about what we have on the left side: we have 3 masses with mass X, so you can say I will give you a few seconds to think about it. That equates what we have on the left hand, with what we have on the right side of the scale. But before we even do that, I want you to think about a mathematical equation that can represent what is going on Now, we are going to figure out what X is. Over here, actually, we have two of them. These three blue things, we also have some of the 1kg masses
Not only do we have these identical unknown masses with mass X, Now we mixed up things a little bit more: on the left side of the scale,
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