Do you have questions about 1st degree equation? It's that student who looks at the account here oh and there's x and he's already desperate because he says: ah math was better when there weren't lyrics, but calm people, because it was thinking about helping them overcome these difficulties that you have in the part of math that has the letter, I prepared the list of exercises that you can find in the description and now I'm going to solve each of the equations step by step. Because then, if you have difficulty, you will be able to identify what you are having difficulty with or if you solved it and made a mistake in some procedure, you will also be able to identify it to rock your activities and already leave your like for today's class, if subscribe to the Gis channel and activate the bell so you can receive notifications, right guys, there's a list of exercises and resolutions, then you can clear your doubts and receive all the notifications of the classes that I publish to help you with the activities.
so take a look here in this case I have an equation why do I have an equation? First because I have the term there which is our unknown, term there which I have unknown, it is our unknown and, I also have an equality, an equality sign. So that's what differs an equation from an algebraic expression.
Ah, another thing too, an algebraic expression, because the students get confused, we have a variable in an equation we have the unknown which is the unknown value ok but how am I going to solve this here? So in this first case, I'm going to make that schematic with the little squares so you can see why we do the inverse operation on an equation when I solve an equation and I also take advantage of it and leave the indication of the class. Class 1 on equations in which I explained everything in detail why we said, ah, on one side it is a sign that undergoes an inverse operation which is what I am also doing with the small square, but there I did it representing the idea of balance using a scale then, be sure to attend this class.
What do you need to know first. Here between the number and the letter that is our unknown we have a multiplication, so the X for us is the unknown value that I will represent by means of a small square What number do I put here in the small square that I do what with this people number that I multiply by two, that's not what I do, then I'll get another value that I do there I add 5 and I get 13 and this little square of mine looks more like a rectangle than a little square. But anyway, so you saw that I always have a result in an equation and then I need to find out what the unknown value is.
And then how do I solve it? What number do I multiply by two that I add 5 to 13? So we're going to do the inverse operation.
Let's do the little arrows going back now oh, the little arrow comes back, so I do the inverse operation 13 - 5 which will be equal to eight right, inverse operation, now the little arrow 8 goes back, the time it went there it was multiplying if it goes back it comes back dividing 8 / 2 here people I want to put eight here 8 / 2 = 4. Ah, but then it means that ox = 4 , yes people ox equals four that's it, I solved it. Ah, but what if I don't want to do the schematic of the square Then let's do it straight Oh!
take the equation I'll write the equation again here for you 2 x + 5 = 13 and you always start with the result. Okay for that number that is on the second member, because after the equal sign which is on the right, we have the second member and before that we have the first member for you who attended that class I already mentioned. You know 1st first member and 2nd member right.
Then what I do I do 13 there you see five here, he wasn't there anymore that's why we say pass to the other side pass negative, pass the changed sign it will pass less. Look here, inverse operation he went plus and he came back minus you see that I do 13 - 5 ah if here it was less then I would do more here 13 - 5 = 8 now what do I do with this eight? These two here are not being multiplied as an unknown for him to get out of there he goes by dividing the 8 and 8 / 2 = four here.
I managed to solve it so x is going to be equal to four in this case here ready people. Second case, what do I have that is different about the letter B from the letter A? You you got it right speaking of the resolution of the letter A, did you get it right here?
Did you get to x = 4? Well done! In this one, what's different is that here I have two terms with an unknown variable, in this case here I only had one term with an unknown variable.
Oh but I can't take these two terms together to make it easier? Come on people, let's put these two terms together here when there's nobody there's one, joining 1 with 2 with 3 we'll get 3, 3 x + 3 = 18 So you see that I've simplified the writing. The statements they bring even with several themes for you to visualize Does the student know what similar terms are, how to put these terms together?
So that's why. Now how do I do it, let's see if you got the hang of it? It will do 18 that here the result I do minus 3, it was more so I do 1 minus which is the same reasoning here 18 - 3 = 15 what do I do now that 3 was not being multiplied with the unknown?
So now I do a division 15 / 3 and 15 / 3 = 5. So in this exercise the x will be equal to 5, because each exercise x will have a value, because each case is a case, right people. Did you hit this one?
If it was right, it already gives a check there, it already gives a check there that it was right or wrong. Do not worry. Take a good look at the detailed solution I did and see where you're going wrong, that then you won't go wrong, let's go to the next ones and now I want to see who got that letter C right, because it's different from the others we did there in the others the number was being multiplied with the unknown, here it is dividing is it different?
Folks, it's the same way to do it every time, you have to think of an inverse operation, so let's start here with 22. So I'm going to do 22 which is for the second member. What do I even do?
It 's plus 5 I do minus 5. It's 22 - 5 is going to be equal to 17 and now that I do this 2 here it's dividing x isn't it? What is he going to do then, the inverse operation of division and multiplication, so he comes here multiplying.
So we're going to get 34. So in this exercise the x is going to be 34, why even if it's 34? Because 17 x 2!
For those of you who are confused and want to do this case in the square that is a little different, square divided by 2 which will give a number, then what do I do, then I do 5 more, I always keep an eye out here and it will result in 22. This is not the situation here, now let's do the inverse operation 22 - 5 is here, 22 - 5 which will be equal to 17 Now what I do, the little arrow returns, it was divided, now it comes back multiplying, now I do x 2. 17 x 2 = 34.
So for those of you who prefer to do it this way, which is more laborious, right people, drawing everything correctly, you can do it, feel free, it will always give the same result, you got it right, didn't you? So look where you did it wrong or which part you didn't understand right? In this other case, it's different too, do you see that one case is different from the other here?
See here we have in the first member, here is the second member, we have a letter in the first member and a letter that is the unknown in the second member and, see that we have numbers alone and a number alone so that means that we will have to put the terms on the same side, so we're going to combine like this! Everything that has the unknown we will leave it in the first member and whoever does not have the unknown will come here for the second so we will regroup it, but from the moment he changes the member he has to think about the inverse operation, so it will be here the 7x that is already here I do not change its sign because it remained in the first member, who goes there to accompany the 7x is this 2x, right? This 2x will leave here and he will accompany his friend 7x but he was less here so when he changes sides he will stay more, inverse operation.
And now the numbers that don't have the unknown which is already 84 that I copy here in the second member I don't change the sign, because he didn't change member, who's going to come up with 84? It's not this 30 it will come out of the first one and it will come here for the second one what is the signal people it comes it was more because when there is no signal here it is more so it will come less. Look how I did it now.
What can I piece together in this question now? Here I can't put these two terms together since they both have the same literal part which are similar so 7+2 is 9, 9x = 84 I get 30 = 54 right doing the join well and now it doesn't look like the one I need subtracting the first one has already gone straight down how do I do it now this nine is not multiplying the unknown so it will pass to the member doing what to the second member? Doing the division so here I do 54 / 9 = 54 divided by 9 is it the same?
Where's the table? Who's good at the table? Very well, it is = 6.
So in this exercise I have that x is equal to 6. Take the real proof, 6x9= 54, look here, do you want to take the real proof on this one? 34/2 of 17 plus 5 = 22, perfect right people!
Did you see how we're getting the hang of it? That's why I brought several cases for you to visualize one by one and compare them when solving your exercises. Our people but here in the letter E the unknown is Y?
but doesn't it have to be just X? Of course not. Who told you it's just X?
It can be any letter because I'm representing the unknown value, so it's common to use X, it's common but not that it's obligatory, okay! Let's fix this equation just like we did with the letter D just now, we have to put it in the first member. So the terms that have an account and in the second who doesn't, or if you want to do the opposite, do you want to do the opposite, put in the second who has the unknown in the first who doesn't?
It might be the same thing, it's just the wrong side So let's go the way we used to. So on the first side I'll leave who has the letter that would be 9 Y. Who goes there with 9 Y?
It's the 14 Y this 14 see that its sign here is being added, here then it will pass there with - 14. It will be 9 Y - 14Y = equal to who people? Like the 10 that is already here on the second side, that's why I don't change its sign and the 8 that is more will be less here, remembering the inverse operation.
What can I do now? Here I have 9 and I owe 14. I can put these two terms together and 9 takes 14.
I have 9 and I owe 14, I still owe 5, my God, I owe 5Y =. Out of 10 I take 8 are 2, now people like what we are used to doing, that's why I already did it here on the first, the letter on the first side just to happen here so you can visualize how we have then the term that is with the unknown if it becomes negative and this other one is positive I'm going to multiply the whole line by -1. You must have already learned that there, multiply the entire line by -1, why multiply by -1?
Because then it will be -1 x - 5 , because - with - gives + 5 so it will be +. And here this 2 is + isn't it + and -? It will be - because I left the variable there with the positive value but could I do that directly?
Could people even do it directly when I explain I do this two is +, then + with - negative result, then do the containment directly, but explaining to you what we do, what is the procedure? Now to wrap it up I know this 5 is being multiplied, so we do it divided. So it's going to be - 2/5, but can you give a fraction?
Of course you can! Fraction is not the number? You can give the fraction yes.
So in this exercise I have Y = a -{2}{5} And in this exercise I did the solution in red, you know, in the others I did it in blue and in the others I did it in red, no problem, right, did you get it right? Did you get it right? Very good for you who got it right and for you who didn't get it right, I don't want to see an ugly face on the screen, because look where are you going wrong?
Where is it that you don't understand for you to fix it, we need to fix it and manage to crush all activities. Combined, right? It's okay!
Where's the smile, are you happy? So it's good people, because this case will also be different, this case was the same as the previous one, now this one is new. How do I do?
What is this 5 in parentheses, pay close attention, when you visualize this here it indicates that five is multiplying the two numbers that are inside the parentheses. Okay then, here I must apply the distributive property of multiplication, aka shower, shower, remember the little shower we used to do? So I'm going to do 5 multiplied with x and 5 multiplied with 2, so it's going to be 5.
x=5x and 5. -2= -10. This 5 is +, + with - in the multiplication gives - = 20.
Ok so far? I made the distribution and arrived at those first very basic cases, right? Oh, what do I do, 20 takes the result and applies the inverse operation.
He was - , so I do + , do you have any doubts? Drw the squares. 20 + 10 = 30, What do I do now at 30?
Was the 5 not being multiplied? So here, we're going to divide 30/5 = 6 Where's the check? Here it also checked.
Who got this one right? So in this exercise, the x will be equal to 6. And let's go to the next one!
Guys, have you ever stopped to look at the size here of the G, you can even do just one on the board, it is quite extensive, but first of all what am I going to do as a strategy, we are going to put it together first. What are the like terms for the first member and after the second? It's already shortening so there's no danger of making a mistake.
Oh, here in the first member I can put this one and this one together, which are similar, so here it's going to be 6+4 is 10 and 10 takes 3 is 7x, look here how I've already reduced and copy this 12 because I can't join the 7x with 12 ok, please, won't you say it's 19x? Why not give 19x people? Because here you have it and here you don't, how am I going to put it together?
It won't! Like on this side here, what can I add on this side? I can add the 12, the 10 and the 8 here, this 5, pay attention, 12+10 is 22 and from 22 I take 8, we will get 14.
So here it will be 14, there + the 5x. Now it's better, because it looks like one of the examples we've seen before where I now need to leave everything that has the unknown in the first member, who doesn't have it, goes to the second. So the first member will have 7x and who will go there with himself 5.
So there will be 5x. Just remembering the inverse operation, it was + then I do it -, you remembered that, right? = on this other side, the 14 is already in the second member, so it doesn't change the sign and the 12 that comes here -12, because of the inverse operation.
And now people, what do I do in this case? Let's add 7x - 5x again here, it will give 2x = 14 -12= 2 and now this 2 that was multiplying we divide it. So it's 2/2=1.
So in this exercise, x will be 1 and I just want to see the smile, who got it right? Give Gis a thumbs up on your side of the screen, or at least give him a smile. Oh, wonderful people!
And for you who didn't get it right, you won't make an ugly face. Stop and look where you're going wrong, that's why this class with the detailed explanation and now I want to see who got the last example right, because it involves fractions and according to some students, if they have fractions, it's difficult. And I'll show you that it's not hard, come on!
So people, when you look at fractions in the equation, you won't run out and say it's hard, okay! Or say it's hard and run away. You have to do it in order, let's take it easy, the first thing to do strategically put 1 down here, now look, you have the denominators 4, 2 and 1, forget the X for now guys, now let's think about the three-quarter fractions + 5 halves = 6 over 1.
How should I proceed? So we must take an MMC between 4 and 2. What is the MMC between 4 and 2 is going to be 4.
So it's going to be 4, put 4 here. So each fraction is written with its new common denominator which is 4, now we are going to do the equivalence process, but why did I arrive at 4? You're asking people, we did the MMC between 4 and 2.
Who forgot the MMC, how do you calculate it? So I already leave the indication to help you. If you are in doubt about how to calculate MMC, there is no point in continuing the equivalence process from here.
It is necessary to go back to the MMC class! Then it went back to MMC and then you came back here again, so here the MMC is 4 let's do the process of equivalence of 4 to become 4, it was multiplied 4 by 1 , right, so that means that the top one will also be times 1 , copy the same thing will not change, 3x now here, from 2 to get to 4 I did it multiplied by 2 and you will confuse it with this multiplied x let's go by point so, no problem, put the multiplied dot, then don't confuse with ox of the unknown. It was multiplied by 2 which gave 4, so here I also multiply by 2, 5 x 2 = 10 and copy the letter x, see how it is not difficult and from 1 to 4 it was multiplied by 4, 26 x 4?
Can you do the math in your head? Gives 26 with 26 =52, 52 + 52= 104, so here it will be, 104. Now there is good news for you every time I do this MMC process and I do equivalence and I have an equation, mark it well, there is than having an equation, you can take the denominator out.
When you have an equation because of the idea of Equilibrium, what If I remove it from the 1st member or remove it from the other side of the scale, it won't make any difference, I took denominator 4 from the first and denominator 4 from the second, it doesn't change anything, what's left for me then? There are now 3x+10x=104 left. What can I do for strategy?
We can then join the 3x and 10x since they are similar and putting them together here we get 13x=104. And now people want to see who's who's ace now! How do I finish and find the value of x?
You're going to get o104 now and what do you do? I divided by 13, because the 13 was being multiplied with the unknown. So it's going to divide by 13.
Do you want to do the division count, who has doubts about the division account? I'll leave a class indication for you too. Does 104/13 give the whole number?
So let's try 13 there, if I take the middle which is times 5, 5x3 gives 15 goes up 1, 5 x1=5 +1=6. 65 is much more, so let's try 13 times, look at a strategy that I use to do this calculation I think, it ended in 4 so what number do I multiply by 3 that ends in 4, it has to be greater than 5, because 5 here, the 7 if I multiply 7 here, 7x3= 21 ends in 1, it doesn't matter, how much 8, 8x3=24, ends in 4, will it be enough? Goes up 2, 8 x1= 8=2=10.
So I think when I do mental calculations I do it like this, it's not because I'm a math teacher, I 've been doing this since I was studying, just like you're studying, then I worked out the strategy in my head to do mental calculations, so here it means that it will be 8x13=104. So it's a mental calculation strategy, each one elaborates which one is better, so I found that x is worth 8, so I put that x is worth 8 and I managed to finish. And then I go there and check the resolution.
Tell me did you get it right? How much? Quite a bit, but let's stop talking, did you get it right or wrong, right?
Let's change the question. Can you now understand how to solve the first degree equation? You saw what I did, there are eight examples and I explained each one of them to you in detail.
And then, in case you didn't understand very well, go back to the videos, in this video or in the previous ones that already have several equation classes on the channel and one more observation for you, in solving these equations, did you see how many previous mathematical concepts I used? Just here for example: MMC, fraction equivalence, division, only in this example apart from the others that we applied in that case the distributive property that was the shower head. So it's important people if you don't know certain content to remember to improve in this case here in what you're studying right?
That's why many say that math is difficult, because you don't remember the previous content, how are you going to do this content here? Ok people, so take the opportunity to like today's class, subscribe to the Gis channel and activate the bell, then you will receive notifications for all the classes that I publish and don't forget to share this class with your colleagues and the exercise list together right guys? And I'll see you in the next class bye bye!
