Representing a relationship with an equation

I now want to re figure out what this mystery mass is but we're going to start using a little bit a little bit more of mathematics and mathematics really are just a language of 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 it'll give you a few seconds to do that so let's think about 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 three kilograms so let me write over here I'll just add we'll assume that we're dealing with kilogram so we have the mystery mass in kilograms plus three 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 one two three four five six seven eight nine ten kilograms so we just have ten we just have ten 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 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 three kilograms to it then we see that it has the exact same mass as ten 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 on the last little problem that we had that if we wanted to figure out this mystery mass we had to remove three of these three kilograms from both sides if we just remove three 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 this stuff has to actually be balanced so in the last in the last video we removed three of these we remove three 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 three naught from one side if we remove three from one side then it wouldn't be equal anymore we need to remove three from both sides so we need to remove three we need to subtract three 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 on the right hand side we're left with 10 minus 3 which is 7 10 minus 3 which is 7 and we get the exact same result question mark is equal to 7 and for dealing with kilograms then this is 7 kilograms