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Alright, now we have a very interesting situation.

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On both sides of the scale, we have our mystery mass and now I'm calling the mystery mass having a mass of Y.

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Just to show you that it doesn't always have to be X.

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It can be any symbol as long as you can keep track of that symbol.

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But all these have the same mass. That's why I wrote Y on all of them.

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And we also have a little 1 kilogram boxes on both sides of the scale.

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So the first thing I wanna do, we're gonna do step by step and try to figure out what this mystery mass is.

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But the first thing I wanna do is, is, is, have you think about, whether you can represent this algebraically?

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Whether with, with a little bit of mathematic symbolry, you can represent what's going on this scale.

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Over here, I have three Ys and three of these boxes and their total mass is equal to this one Y.

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And I think I have about let's see, I have 7 boxes right over here.

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So I'll give you a few seconds to do that.

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So let's think about the total mass over here. We have 3 boxes and a mass Y.

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So they're going to have a mass of 3Y, and then you have 3 boxes with a mass of 1 kilogram.

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So they're going to have a mass of 3 kilograms. Now over here, I have 1 box with a mass of Y kilograms.

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So that's going to be my 1Y right over there. I could've written 1Y but that's, I don't need to.

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A Y is the same thing as 1Y. So I have the Y kilograms right there. And I have seven of these, right?

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1,2,3,4,5,6,7. Yup, seven of these. So I have Y plus 7 kilograms on the right-hand side.

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And once again, it's balanced. The scale is balanced. This mass, total mass is equal to this total mass.

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So we can write an equal sign, right over there. So that's a good starting point.

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We were able to represent this situation to this real-life simple situation.

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You know, back in the day, when people actually had to figure out the mass of things if you were to go the jewelry store, whatever.

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They actually did had problems like this. We were able to represent it mathematically.

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Now the next thing to do is, what are some reasonable next steps? How can we start to simplify this a little bit?

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You know, once again, I'll give you a few seconds to think about that.

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Well, the neat thing about algebra is there's actually multiple paths that you could go down.

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You might say, well why won't we remove 3 of these what, of these yellow blocks from both sides?

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That would be completely legitimate. You might say, well, why won't we remove 1 of these Ys from both sides?

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That also would be legitimate. And we could do it in either order. So let's just pick one of them.

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Let's say that we've first want to remove, let's say that we first want to remove the, a Y from either sides.

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Just so that we feel a little bit more comfortable with all of our Ys sitting on the 1 side.

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And so the best way, if we don't want all of our Ys to sit on the 1 side, we can remove, we can remove a Y from each side.

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Remember, if you removed a Y from only 1 side, that would unbalance the scale. The scale was already balanced whatever you have to do to the one side after you do the other.

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So I'm gonna remove a Y, I'm gonna remove Y mass from both sides. Now what will that look like algebraically?

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Well. I remove the Y from both sides. So I subtracted Y from the left-hand side and I subtracted Y from the right-hand side.

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That's exactly what I did. The mass, it had a massive Y. I don't know what that is but I did take it away.

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I lifted that block, that little, that little block. And so, on the left-hand side, on the left-hand side, what am I left with?

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That you can pick it up mathematically, you can even look up here, and look up here what you're left with.

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If I had 3 of something, and I take away 1 of them, if I take away 1 of them, I'm left with 2 of that something.

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So I'm left with 2Y, right over here, you see it. I had 3, I got rid of 1, so I'm left with 2.

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And I still have those 3 yellow blocks. So I still have those 3 yellow blocks. On the right-hand side, I had a Y, I took away the Y, and so now I have no Ys left.

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We see it visually right over here. And I still have 7 of the yellow blocks. So I still have 7 of the yellow blocks.

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And since I took the exact same mass from both sides of the scale, the scale is still going to be balanced. It was balanced before, I took away the same thing from both sides.

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And so the scale is still, is still balanced. So this is going to be equal to that.

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Now, now just trying to look a bit similar to what we saw in that last video.

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But I will ask you, what can we do from this point?

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What can we do from this point to simplify it further or so, even better, think of it so we could isolate the, these Ys on the left-hand side.

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And I'll give you a few seconds to think about that.

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Well, if we want to isolate these Ys on the left-hand side, these 2 Ys, the best way is to get rid of this 3, to get rid of these 3 blocks.

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So why won't we do that? Let's take 3 blocks from this side but we can't just take it from that side if we want to keep it balanced.

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We have to do it to this side too. We gotta take away, we gotta take away 3 blocks.

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So we're subtracting 3 from that side, and subtracting 3 from the right side.

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So on the left-hand side, on the left-hand side, we're gonna be left with just these 2 blocks of mass Y.

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So our total mass is now going to be 2Y. These 3 minus 3 is 0, and you see that here.

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We're just left with 2Ys right over here, and on the right-hand side, we got rid of 3 of the blocks.

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So we only have 4 of them left. So you have 4 of them left. So you have 2 of these Y masses is equal to 4 kilograms.

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And because we did the same thing to both sides, the scale is still balanced.

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And now, well how do we solve this? And you might be able to solve this in your head. I have 2 times something is equal to 4.

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And you can kind of think about what that is, but if we want to stay true to what we've been doing before, let's think about it.

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I have 2 of something, is equal to something else. What if I multiply both sides by 2?

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Oh, sorry, what if I multiply both sides by 1/2 or another way is dividing both sides by 2.

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If I multiply this side by 1/2, if I essentially take away half of the mass, or I'll only leave half of the mass,

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Then, I'm only gonna have 1 block here, and if I take away half of the mass over here, I'm gonna have to take away 2 of these blocks right over there.

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And what I just did, you could say I multiplied both sides by 1/2 or just for a sake of a little change,

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You could say I divided both sides by 2. And on the left-hand side, I'm left with a mass of Y.

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And on the right-hand side, I'm left with a mass of 4 divided by 2 is 2. And once again I can still write this equal sign because the scale is balanced.

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I did the exact same thing to both sides. I left half to what was on the left-hand side, and half of it was on the right-hand side.

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It was balanced before, half of each side, so it's going to be balanced again. But there, we've done it.

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We've solved something that's actually not so easy to solve. Or it might not look so easy first.

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We figured out that our mystery mass Y is 2 kilograms. And you can verify this, this is the really fun thing about algebra.

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Is it, once you get to this point, you can go back and think about whether the original, the original problem you saw made sense.

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Let's do that. Let's think about whether the original problem made sense. And to do that, I want you to, I want you to calculate.

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Now that we know what the mass Y is it's 2 kilograms. What was the total mass on each side?

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Well, let's calculate it. We have 2 right, right over here, this is 2 kilograms, I'll do that in purple color,so this is a 2, this is a 2, this is a 2.

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So we had 6 kilograms plus these 3, we had 9 kilograms on the left-hand side. And on the right-hand side, I had these 7 plus 2 here, 7 plus 2 is 9 kilograms.

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That's why it was balanced. Our mystery mass, we had 9 kilograms, total on both sides.