Hi guys, did you know that equations are important foundations in mathematics? That's right, they are used to solve a variety of problems in our daily lives, so are you curious and want to learn more about this content? So come with me.
. . So welcome to my channel, I'm Gis and in this class I'm going to explain 1st degree equations.
So this is class 1, okay guys, a sequence of classes. So let's go, when I study equations I have to think about the idea of balance and it's common for us to start studying equations using a scale, look how beautiful my scale turned out, right this scale of mine is in balance, what does it mean to be in balance? It means that the same amount of mass that is here is the same amount that is here, right, okay, the same measurement here is the same measurement here, now let's try to find out what the weight of each blue square is, knowing that each little ball has a mass of 1 kg, And then can you guess how much is in each square, how much does each square weigh?
Let's go then, what do I have to do, as my scale is in balance, I know that the same amount of mass that is here is the same amount of mass that is here, so I'm going to start doing the following, I'm going to take a little ball from here this little ball weighs 1kg it has a mass of 1 kg and now my scale what happened to it should then go into imbalance because I took a little ball from one side it wasn't that so now automatically if I take it from here and I take one from here what What happens is that the scales come back into balance, right, because I took the same thing from each plate, and now I can take one more ball from here, right ? so this little ball has to stay there, I can't take out what I can take out of there, so guys, I can take out this little box which is this little blue square, and then if I take out a little blue square from here the scale gets unbalanced because I only took it from one side, so what I take from one side I also take from the other side. So, look, I took it from one side and took it from the other side, which means that my scale is balanced, which means that the same mass measurement here is the same as here and now you can identify it, I said that each ball has mass of 1 kg and now here there are 1 2 3 4 5 6 kg so this side here has six kilos, isn't it and here I have two squares two little boxes that whatever and the scale is in balance if it is in balance it is because it has the same measurement on each plate and now people, if two squares weigh 6 kg, one square only weighs as much as one square only weighs as much .
algebraic, which is algebraic thinking folks, personally algebraic is when I think about the unknown term because I didn't know the value here and then I solved it by square until I found its value so I had algebraic thinking, I had a value unknown beauty? now we are going to write this same situation that I had from the beginning using the equations in fact we are going to use an equation for now, and what is an equation now guys what do we have to know in an equation we have to know the following all the equation has an equal sign between the two expressions, well, they are expressions for you who attended the algebraic expressions class, I will leave an indication here for you, an algebraic expression is an expression that has letters, numbers and has operations , wasn't that the case at the beginning you studied numerical expressions which was a numerical expression a numerical expression was an expression full of operations, right there was addition and subtraction there was multiplication and division then you started studying algebraic expressions which happened differently than numeric for algebraic algebraic put letter inside, right, and in the algebraic expression we used letters as variables, fine, so far so good. Now we move on to the study of equations and all of this is in the field of algebra, every time I work with the unknown value with letters in mathematics I study algebra ok, so what?
When I study an equation I also have an expression because look at expressions so I have expressions, I have algebraic expressions that have letters but between these algebraic expressions I have an equal sign so that is the main characteristic of an equation is to have the sign of equality, that's why I brought up the concept of scales, the idea of balance, beauty and now this letter that I use in the equation is not called a variable, it is now called an unknown, because in that situation it can only assume one value, okay? it is not the same in the variable as it could assume several values in the equation, the letter then represents the unknown value and this letter is called the unknown, so for you, everything is written here for you to memorize later, ok. Now we're going to take and write this situation the way it was at the beginning with an equation, let's go.
. . Guys, now we're going to solve the same situation that I brought at the beginning, but now we're going to use the equation, so what I said at the beginning that each ball had a mass of 1 kg, remember, the mass of each ball has a mass of 1 kg, cool, so what does the equation that represents this situation look like now, so we know that the scale is in balance So I have an equal sign to represent balance, okay, what can I do here?
I don't know how much each ball is worth, I already know, so who will be my unknown? My unknown here will be the little boxes, right, the blue squares, so I'm going to call each blue square X, very well, so this blue square of mine is X, this other one is X, this other one is X, and this one is X , because they are all the same beauty look what I have now tell me here I have 3 x, 3 squares of x so I 'm going to write here 3 times the square plus a little ball, but a little ball weighs 1 kilo, so plus 1 is not that, this is what is on the first plate of the scale, the same because it is in balance than what I have on the second plate of the scale, I have 1 square X, so there is 1 square we form here, see that here we have an algebraic expression, this here is called the first right term which is there in the first pan of the scale and what was here in reference to the second pan of the balance we call it the second term, ok when I work with the equation so you know the names, and now I need to solve this equation to find out the value of X, so that's what solving an equation means is finding the value of x that satisfies my situation that I brought here ok, So guys, what can I do, so look, let's do it step by step, here's my equation so I'm just going to rewrite it here so we can solve it, 3 x + 1 = 1 x + 7 which I did on the scales I didn't take a dot from here, that's not it, a dot is worth 1 so I subtracted it, I went there and subtracted it, I took it so I took a dot here so minus 1, there was no dot left, oh one minus one, it was zero, that's fine, just what What do I have to do now guys because if I took this little ball out of here my scales became unbalanced this side is heavier so the scales come back into balance What do I have to do I have to come here and take out a little ball too, that's not all here in the equation if I took one ball from here I have to subtract one ball here from seven too and how many did I get now one two three four five six, so seven minus one will give 6 let's rewrite what I have now 3x here we got zero, I don't need to write more equal to 1 x + 7 take away one, it's 6, check here now this second line of mine if it's consistent with what I have on the scale now, three weight x 1 2 3 beauty first member is right here on the second plate one weight x which is the second member here in our equation 1 2 3 4 5 6 and 6 okay what I can do now now I can come here and take this weight from here this weight he from here so he zeroed it beautifully by taking this weight from here, right, the scales got out of balance, what do I have to do, so I have to come here for the scales to stay in balance, right, the idea of solving an equation is always to keep the scales in balance, I took another weight from there so the scale is in balance again, which now leaves 2x but I didn't do something, I didn't take it out of the equation so I have to come there too and subtract 1x whenever I have to do this, you can see what I'm doing here in the equation and there on the scale at the same time so you can understand this reasoning, and now guys what's left here 3x take one out of three I take one out there's two left so here for me there's 2 x left the same on this side there's six left there's no six left now follow along, what I have written here in the equation is not the same thing that I have here on the identical scale and now how do I finish how do I find the value of x if two weights x is worth 6, 2 x is worth 6. 1 will only be worth how much , half is not, so it means that I divide here by two divide here by two 2 / 2 gives 1, 6 / 2 of 3 so what does it mean what I will find here means that x which is 1x, because 2 divided because 2 is 1, 1x then you'll get used to the fact that when I've written 1x, we won't even write that 1 but here it will just look like this, just x, okay, but you can write it normally, it 's not wrong, so I know that 1x = 3 because 6 divided by 2 of 3, so I found the value of my unknown, which was that letter that represented an unknown value.
Let's check, let's validate to see if it's right, I know that each x is worth 3, 3 plus 3 is 6 and here is one, two, three, four, five, six balls weighing 1, so here is six, and here is six, this means that the answer I I found it for my equation is ok. Let's do one more example, let's go. .
. Guys, now we're going to solve the second example, also making the scale and the equation here at the same time so you can relate the two things, okay, so what do I have here in this situation again, so here we are going to consider the mass of the ball to be one kilo each, okay, the tiny ball and this little ball here, this ball is actually worth 8, okay, and then what is the equation that represents this situation here on the scale, let's write then the what do I have on this pan of the scale , that is, on the first member of our equation I have one two three weights x so three weight that I have on this plate plus the weight 8 beauty and then the scale is not in balance so it is equal, remember who one of its main characteristic equation is to have the sign of equality between the two expressions that I have on this second plate of the scale a weight x, oh a little weight What do I do, let's go and do the scales so first thing if I take this weight 8 out of here what will happen I took 8 out of here I also have to go to the scale to stay in balance take eight out of here oh so one two three four five six seven eight, I took 8 weights from there ok the scale is in balance so let's write this here in our equation now, so what did I do I took 8 from the first plate which is the first member of our equation 8 take away eight will zero , note that no one will be here, okay, but then I went there in the second dish and also subtracted 8, I got eight, okay, I always do the inverse operation, you have to think about the inverse operation, okay, so what happens now in my situation? balance what's left for me, let's rewrite: then there's 3x left in that first plate equal to 1x plus here there's left that one two three four which is 12 take away 8 12 - 8 are 4, and now how am I going to solve how I I'm going to find the value of x, which is our unknown, I'm going to come here, I'm going to take a weight a weight x of the second member that corresponds to our second plate, then I also go there and take a weight x because then our scale goes stay in balance so don't forget come here and also take a weight equal here one minus 1 is zero, you can see that there is no more weight x here and there are four left here, ok so two weights x = 4, 2 weight x = 4 perfect so we will do both things together so you can understand, how I finish now there I have so if two weight x is worth four one weight x is worth how much is half it is not divided by two so here why when I divide by two is not multiplying by 2, X is not being multiplied by 2 what is the inverse operation of multiplication is division so that's why I come here I divide by two then 2 divided by 2 gives 1, 1X but people, every time what I do on a scale pan I do on a member of the equation in the If I divided by 2 here I have to do it on the second member too so I divide by two there too 4 / 2 are two and what does this result mean, found that one x, that is, one weight X is equal to two balls, which is equal to 2 and then, our scale is in balance and I managed to find the solution to our equation which is x being 2 and then you remember that I said that writing just one x like this is the same thing as me writing just x, x = 2 so any of the ways you write here for x have the same meaning, okay guys?
So, I hope you understood this class I did with the scales, you know, creating the idea of the scales in balance, already writing the equation here on the side, I hope you understood, you liked my explanation, and don't forget to subscribe to Gis' channel and leave a thumbs up for me, and I'll be waiting for you in the next class on equations. Until later. .
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