Dividing both sides of an equation

so we have our scale again and we've got some masses on the left-hand side and some masses on the right-hand side and we see that our scale is balanced we have the same total mass on the left-hand side that we have on the right-hand side instead of labeling the mystery masses as question mark I've labeled them all X and since they all have an X on it we know that each of these have the same mass but what I'm curious about is what is that mass what is the mass of each of these of each of these mystery masses I guess we could say and so I'll let you think about that for a second how would you figure out what the mystery mass but what each what this x value actually is how many kilograms is the mass of each of these things what could you do to either one or both sides of this scale and I'll give you a few seconds to think about that so you might be tempted to say well if I could end up with just one mystery mass on the left-hand side then it's going to be equal to and if I keep my scale balanced then that things going to be equal to whatever I have on the right-hand side and that part would actually be a true statement but then to get only one mystery of one of these mystery masses on the left-hand side you might say well why don't I just remove two of them you might just say well let me just remove why don't I just remove we do it a good color for removing why don't I just remove that one and that one and then I'll just be left with that right over there but if you just removed these two then the left-hand side is going to become lighter or it's going to have a lower mass than the right-hand side so it's going to move up and the right-hand side is going to move down and then you might say ok I understand whatever I have to do to the left-hand side I have to do the right-hand side in order to keep my scale balanced so you might say well why don't I remove two of these mystery masses from the right-hand side but that's a problem too because you don't know what this mystery mass is you could try to remove two from this but how many of these blocks represent a mystery mass we actually don't know but you might then say well let's see I've got three of these things here if I if I essentially multiply what I have here by a third or if I only leave a third of the stuff here and if I only leave a third of the stuff here then the scale should be balanced if this has the same mass if this has a total mass as this then one third of the total mass is going to be the same thing as one third of that total mass so let's remove so let's just keep only one third of this here so that's equivalent to multiplying by one third so if we're only going to keep one third there we're going to be left with only one of the masses and if we only keep one third here let's see we have one two three four five six seven eight nine masses if we only if we multiply this by one-third or if we only keep 1/3 of it they're one-third times nine is only three or it's three so we're going to remove these and so we have one third of what we originally had on the right hand side and one third of what we originally had on the left hand side and they will be balanced because we took one-third of the same total masses and so what you're left with is just one of these mystery masses this this X thing right over here whatever X might be and you have three kilograms on the right hand side and so you can make the conclusion and the whole time you kept this thing balanced that X is equal to three