This equation seems impossible to solve !

Ajouté : 2026-05-15

[00:00:01]Hello, welcome back once again. Today we have this interesting algebraic equation.

[00:00:07]We have to find the value of x given that x minus two divided by two minus x is equal to four.

[00:00:14]So, let's get started.

[00:00:17]Now, listen guys, an equation does not have a solution does not make the equation useless or meaningless, okay?

[00:00:26]Now, in this case here where you ask to find the value of x and maybe the equation doesn't have a solution.

[00:00:32]Sometimes this is a normal way to check your level of of understanding of mathematics.

[00:00:40]Okay, now let's proceed.

[00:00:42]Here we're going to find the value of x, but take a look on this left-hand side.

[00:00:47]Actually, x cannot be two, right? If x is equal to two, we're going to have two minus two at the denominator, which will make it zero. And division by zero will make this left-hand side undefined. So, we need to take note of that.

[00:01:00]Now, actually here we can actually factor out negative one from the numerator. If you factor out negative one from the numerator, we're going to switch this to two minus x.

[00:01:12]And then at the denominator we have two minus x. So, this is equal to four.

[00:01:19]And we can see from here this both get cancelled and here we have this first equation negative one is equal to four.

[00:01:27]And we know this is false.

[00:01:32]So, what is going on? Does it mean that with this method here we just arrive at an equation that is false? We know this is not true.

[00:01:41]Or does it mean there's no solution? I think let's just label it that there's no solution.

[00:01:47]But what happens when we cross multiply the equation? Let's see.

[00:01:51]So, from the original equation we have x minus two divided by two minus x.

[00:01:58]This is equal to 4 divided by 1. So, let's cross multiply. So, here 4 or x minus 2 times 1 here will give us x minus 2 is equal to 4 multiplied by 2 minus x.

[00:02:13]From here we get x minus 2 is equal to 8 minus 4 x.

[00:02:20]Now, let us collect like terms. So, here we have x. So, this one is negative crossing over becomes positive 4 x.

[00:02:28]Is equal to here 8 is positive. This one is negative crossing over becomes positive 2.

[00:02:34]From here we get 5 x is equal to 8 plus 2 will give us 10.

[00:02:39]So, divide both sides by 5.

[00:02:43]This both get cancelled. From here, we have that x is equal to 2.

[00:02:49]But earlier, we stated that x cannot be 2 because of the denominator. Our left hand side of the equation is x minus 2 divided by 2 minus x. So, it clearly implies that 2 cannot be a solution because it will make this left hand side undefined. Therefore, 2 is an external solution when you cross multiply.

[00:03:09]So, in this case this equation doesn't need any cross multiplication. We just factor out negative 1 from here and cancel out and you arrive at just negative 1 is equal to 4, which is probably wrong, right? So, therefore, the best solution to this problem is that there's no solution.

[00:03:30]There's no solution. Thank you for watching. If you enjoyed the video, please kindly subscribe to this channel.

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