Can you solve this equation?

Hello my lovelies, it's Susanna and today I want to show you how to solve this equation. It's an easy one actually, but I asked my family and friends how they would solve it and yeah, it doesn't seem to be that easy as an adult anymore. So let's see how to solve it properly. We have x equals x over 5. So we have x on both sides and we have this fraction here. So maybe first of all we get rid of the fraction because usually people don't like fractions. We have x divided by 5 so we get rid of it if we multiply both sides by 5. Then we have x times 5 which equals 5x and on the other side this 5 cancels with this 5 and x is the only thing that's left. So no fraction anymore. Okay now 5x equals x. What most of the people did, don't do it, I do it in red, but I want to show you what they did. They said oh we have x on both sides so we can just divide both sides by x and then x cancels out. Be careful with that if you don't know what you're doing. You can do it if you do a case distinction then but if you're not sure what you're doing better not do it. I'll show you another way later but let's see what happens. So we cancel out x. 5 is the only thing that's left on the left side and here we have x divided by x which equals 1. 5 equals 1. What does that mean? Well this is not right. That just means that we don't have a solution for this equation. So we would say there is no solution to this equation but is that right? Let's go back to this one and see how to do it properly. This is just a linear equation. We have x on both sides and a linear equation you usually solve it by putting all the stuff that has x to one side. So we would take this x and put it to the other side by subtracting x. So we have 5x minus x equals 4x and on the other side x minus x equals 0. Now we have x on just one side here and if we want to solve for x we just have to get rid of this 4 here. We have 4 times x so we divide both sides by 4 to get rid of it. 4 cancels out. x is the only thing that's left and here we have 0 divided by 4 which equals 0 and we see there is a solution. 0 is the only solution for this equation here. So what happened? Why didn't we find this solution when we divide it by x? Well we don't know what x actually is, right? x could be any number and x could also be 0 and if x was 0 then we would divide by 0 which is not a good thing to do in mathematics. So we would have to do a case distinction to see okay if x equals 0 what would happen then and then we would find this solution as well what we find here as well with this way here. But I think this is the easier way than the case distinction and usually you don't think of that. So better not do this. Never divide by your variable if you don't know what you're doing. But yeah I hope you enjoyed it. If you have any questions please let me know in the comments. I wish you a wonderful day and I hope to see you in one of my next videos. Take care!