Introduction to solving an equation with variables on both sides | Algebra I | Khan Academy

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Let’s try to solve more equations Let’s say we have 2x plus 3, 2x plus 3 is equal Equals “5x – 2” This equation appears difficult at first sight We have x on both sides of the equation We add and subtract numbers How can it be solved? We can solve it in more ways than one The important thing that we must remember is that we are only We want to isolate x By isolating x you would have found x equal to something Or x equals a certain thing And you’ve finished, you’ve analyzed the equation. So you can go back and make sure it works, then What we will do is a bunch of operations on Both sides of the equation to isolate x But while doing this, the truth is I want to make you visualize What is happening? Because I do not want to say: What are the rules Or the steps to solve the equation And I forgot whether or not this step was permissible If you display what is happening, it will happen It is common sense So let’s visualize it We have 2x here on the left side It is literally x plus x Then you have positive 3 Plus 3, I’m going to write it like this This equals positive plus 1 plus 1 plus 1 It is the same total 3 I can draw three circles here as well Let’s paint it in the same color Plus 3 Hence this is equal to 5x Let’s draw it in blue This is equal to 5x So 1 2 3 4 5 To make it clear And you shouldn’t do it this way You solve the equation You must take algebraic steps But I’m doing this for you to visualize And what does the equation say On the left side are these orange x plus 3 On the right side 5x minus 2 So minus 2, we can write it as … I’m going to make it In a different color So minus 2 I’m going to write it as minus 1 minus 1 Now, we want to isolate x on the same side From the equation So how do we do this? Well, there are two ways to do this We can subtract these x from my side The equation This is logical Because you will have 5x minus 2x And you’ll have a positive number of x on the right side Or you can subtract 5x from both sides This is beautiful in linear algebra If you do the right operations, you will find The correct answer So let’s subtract 2x from both sides The equation And what I mean here, is that we’re going to remove 2x From the left side If we move 2x to the left side, it is necessary Removed from the right side So So what do we get from this We are subtracting 2x From the left And we’re also subtracting 2x from the right Now, to what is the left side short? We have 2x plus 3 minus 2x And x cancel each other out So we have 3 left And you can see that here We took 2 of these x and set them aside We stayed with 1 plus 1 plus 1 And then on the right side 5x minus 2 You can find it here We have 5x minus 2x It remains 1 2 3 x 3 equals 3x Here you have a negative 2 You have minus 2 Usually if you want to solve the problem, you just have to Write what we have written here on the left side So what are we going to do now? Remember, we want to isolate x So we have all x on the right side here And if we could just get rid of minus 2 from The right side, x will be alone It will be isolated How can we get rid of minus 2, if we do Imagine it here This is negative 1 and this negative 1 Well, we can add 2 to both sides of the equation Think about what will happen here If we add 2, I will do this as follows Plus 1 plus 1 And you can see this We collect 2 And we are adding 2 on the left side 1 plus 1 plus what’s going I will do it here So we are adding 2 We collect 2 What will get on the left side? 3 plus 2 equals 5 That would be 3x minus 2 plus 2 These two cancel each other out And we only have 3x We can see that here We have the left side 1 plus 1 plus 1 plus 1 plus 1 We have 5 units or 5 On the right side we have 3x Here And we have minus 1 minus 1 Plus 1 plus 1 minus 1 eliminates some The result is 0 Cancel some of them So we get 5 equal 3x So we have 1 2 3 4 5 equal to 3x I will remove everything for our language, to become Explained These are all things that we have removed. Let me clarify this. And then let me clarify this, like this .. Release. Clear. So far we’re only with 1, 2, 3, 4, 5. Actually, let me move this above. I can even move this here. We now have 1, 2, 3, 4, 5. These are the two that I add here, equal to 3 x. These have been canceled. That is why we have nothing there. Now, to solve this equation, we just divide both sides From this equation that 3. This will not be a little difficult Imagine it here But if we divide here by both sides 3, what do we get? Divide the left side by 3. And right over 3. The whole reason why we divide by 3 is x Multiplied by 3. 3 is the coefficient for x. A luxurious word, literally means only the number Multiplied by the variable. The number we solve, and the variable we solve Abolish these 3. The left side of the equation is only x. The left side is 5/3. So 5/3, and we can say 5/3. This is different from everything we’ve seen so far. And now, x is on the left, its value On the left side. This is quite good. This is the same thing as saying that 5/3 equals x The same thing saying x is equal to 5/3. Completely neutral. Sometimes we are used to using this one, but this one Quite the same. Now, if we want to write this as a mixed fraction, if we want To write this as a mixed fraction, divide 5 by 3 times one With the rest 2. So it’ll be 1 2/3. So we could also write that x is equal to 1 2/3. And I will leave for you to be a substitute for reality back In this original equation. And see if it works. Now, imagine that he’s here, you know, how he gets 1 2/3, let’s think about that. Instead of doing 1, I’m going to do it like circles. I’m going to do it as circles. Actually, even better, I’m going to do squares. So I have 5 squares on the left side. We will do it in this yellow color here. I have 1, 2, 3, 4, 5. Which will be equal to x 3 signs x plus x plus x. Now, we’re going to divide both sides of equation 3. We’ll divide both sides of equation 3. In fact, we did this here, and we We’ll divide both sides of equation 3. So how do we do that beautiful left side directly. You want to divide these signs into 3 x 3 groups. That is 1, 2, 3 groups. 1, 2, 3. Now, how do you divide 5 into 3? And they have to think of some by marital groups. And tell us the answer. Each group will be 1 2/3. So, 1 2/3. So it’ll be 2/3 of this, the next one. Hence we will be 1 2/3. So this is 1/3. We’re going to need another one. Another 1, so this is 1 1/3. And we’re going to 1 need more than 1/3, so that’s going to be To be here. And then we left with 2/3 and 1. We even broke it into 3 groups. This is here. Let me make it clear. Allow me to make it clear. Here 1 2/3. 1 2/3. And then here, this is 1/3. This is the last 1/3, so that’s 2/3, then This is 1 over there. This is 1 2/3. And then finally this is 2/3, and this 1, so this is 1 2/3. Even when dividing both sides by 3 you can get 1 2/3. Each clip, or bucket, is 1 2/3 on the left side. On the left side, or 5/3. On the left side, we just have x. And still working. Slightly difficult to visualize with fractions.

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