Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
I was curious. So, if we rearrange thi equation, we get 5 =x/x And if we substitute the solution- the value of x = 0, it should be satisfied. Right? What do they call equations whose variable values satisfy them and also do not satisfy them?
@@Dreosaurus Thanks, I understand. But that was my point since x=0 is the solution, why does it not hold when the equation is re-written in the other form?
I am 67 and always had a keen interest in math in the sense that math is a numerical form of measurement of the physical world in which we live. Although, I love math I was never really all that good at it. Well, in high school I got by. Perhaps I am just very rusty at it now after all of these years. And that is where you and your wonderful channel comes in. Thank you, Math Queen, for helping me in my journey of kicking the mathematical rust off.
This is demonstrating the classic pitfall of dividing by an unknown value where that value could be zero. Mathematical fallacies where starting with an equation and going through a list of apparently logical steps results in something like 2=1 often involves dividing by zero at one step.
Susanne, your solution is mathematically convincing. However, the fact that only zero fits is actually evident at first glance because one-fifth of x can never be x, except when x is zero.
While it is evident (provided your numeracy skill is sufficient to deduce that) you haven't solved the equation. To solve the equation you need to do what she did, which is get x on its own on one side and a value on the other. Knowing the answer != solving the problem.
That's not the point of this channel. It's not about mathematical rocket science, but rather about making it accessible to an average high school student.
Місяць тому+8
It's more than convincing. Your approach could be to factor out x. x•1 = x•(1/5). That is x(1=1/5), (making "sense" only for x=0) or more systematically -- like in the video; x(1-(1/5)) = 0, x(4/5) = 0, x = (5•0)/4 = 0. It's important to work up a number sense like you have done. But it's also vital to learn to be formal. Then one can communicate knowledge better and also interpret knowledge better.
@@Coolmoed graphical solutions help sometimes because one can literally visualize just how verified the solution is... It's just another tool that some people prefer.
@@Coolmoed more work is absolutely welcome if it helps something stick for someone. It's not always about getting the answer just to say you did. Some students actually care about gaining a deeper understanding of the overall, which includes reconciling across multiple methods sometimes.
As a communications and electronics engineer grad and math enthusiast for years, I can wholeheartedly say that this channel was sth I absolutely NEEDED to see. It helped me remember after such a long time what the applying the basics actually looked like, using the most basic of steps instead of just the advanced type I'm already used to reminded me of the insights doing more basic steps gets me. I thank you from the bottom of my heart for once again reminding me of the beauty of even the simplest and most basic parts of maths.
One other number that works is infinity because infinity is equal to infinity/5. its the same concept as dividing by 0 because any number divided by 0 is infinity. This answer is as valid as x=0.
That was the conclusion I came to - I haven't watched the video, but I multiplied each side by 5, then it has to be x = 0, or x = infinity, since 5 * infinity = infinity. Prove me wrong, somebody!
As an engineer I knew it was zero but did the work to see why. But I agree...Kids in the USA are behind in math for many reasons and memorization is one of them
I've just come across your channel in the last few days, I'm 56 now and it's nice to pause your video at the start and then try and work your sums out. Also to look at how you solve them. Thanks for demonstrating what happens if you try and cancel out x when you don't know what it is. For my part I'd figured if you solve for x then the last thing you want to do is cancel x out of the equation. and once you remember that 0 divided by anything = 0 the equation becomes very easy to solve.
Love the contrasting solution attempts. It's always good to remind oneself that when you divide by the variable x, you need to exclude the x=0 solution. But that doesn't mean you don't check to see if x=0 is a solution, which in this case would immediately show that it's a solution. That said, as a retired math teacher, I really appreciate that you point out that both x and x/5 are linear functions, so to collect the like terms on one side. Voilá! Thanks!
This may all seem very dumb, but it goes to demonstrate that blindly applying rules and techniques won't necessarily solve every math problem. And yet this is what kids learn at school: blindly throwing out memorized rules instead of pausing for a moment and actually thinking.
Disagree; the solution is to use a BETTER set of memorized rules and apply them blindly. The better rule, in this case, is to put everything on one side and factor, and not cancel variables out.
Wonderful. I saw x=0 immediately but I was wondering if there could be another solution in complex numbers. You showed convincingly that 0 is the only solution.
I actually paused the video trying to figure out the right answer, but couldn’t find it. I think I was so stuck in the thought of not understanding an equation could be “impossible”. Thanks Math queen for learning me this!:)
X= X/5 therefore (subtracting X/5 from both sides) 4X/5 = 0 therefore (multiplying both sides by 5) 4X = 0 therefore (dividing both sides by 4) X=0 QED
I just got an expression 5x=x and was like "0 is the only number that can be multiplied by a constant and remain itself, therefore the answer is 0" but then I understood that its not a "solution" technically and I "guessed" the answer. Was actually curious how to *solve* solve it. Been years since I subtracted from equations lol
"We're never gonna use this stuff!" If you think this know that I use math and algebra regularly for finance and in my job, mostly involving electrical/electronic calculations. Basic algebra makes it easy to calculate your range in a car, boat, or aircraft. I used trig and algebra to figure out how many boards to buy and at what angles and lengths to cut the rafters for a shed I built. It cost maybe 20% for me to build it rather than pay others to do it for me. It also feels great to build things. Every cool thing we have is built on math.
@HNH421 I've been interested in math all my life, and trust me, math is built on the weirdest stuff imaginable! It's a good thing I think weird stuff is cool. :)
@@randyduncan795 I am of the opinion, that most philosophy is Sophistry, referring to its use, of fallacious arguments, misleading language, and rhetorical tricks to deceive or manipulate others. but I do not believe in other people, because I am a solipsist, a philosophical idea that suggests one’s own mind is the only true reality, and that all other people and external objects are mere creations or projections of my own mind. So the question remains why am I replying to my Self in this comment section ? The answer is because I am a somnambulist that is asleep.
Thank you! I've been falling in that pit for 30+ years and never knew *why* it happened. Now I do, that's going to make everything easier. Brilliantly explained.
The division by x route is actually very fast. Any time you divide (or multiply by the inverse) you must check that an inverse exists. In other words, you check to see if x = 0 is a valid solution. It is valid so no further algebra is needed.
At first I thought 'How does she spin out this easy equation for a 4 minute video?' but when I actually watched it, your approach of showing the wrong way to tackle it makes sense educationally. Division by zero errors are very important to avoid!
Dividing by x is in many cases the only to procede so you must know how to do this properly, i.e treating the case x=0 seperately. It’s really a special of the very useful zero product rule
Another way is with geometry, x=x/5 means finding all the x-es where the two curves have the same y, y=x and y=x*1/5, so the only x where they have the same y is x=0.
The greatness of dividing by 0 : If you divide by a Zero, you create an absurd answer. Great choice of video ^^ -Early secondary school : x = x/5, x - x/5 = 0, x.(1-1/5) = 0 as (1-1/5)>0 then x = 0 -Middle secondary school : where f(x) = x crossing with f(x) = x/5 ? Only when x = 0
I'd have like to seen the generalization that dividing b y the variable is a bad idea not just "if you don't know what you're doing," but rather especially if you might be dividing by zero because yes, that's when you get "solutions" like 1 = 5.
5x = x 5x - x = 0 4x = 0 x = 0 😊 Another approach: 5x - x = 0 x(5-1) = 0 from here it's either x=0 or 4=0, as 4 most certainly can't be 0 so it must be that x=0
@@SmallSpoonBrigadethank you! I'm sitting here going crazy trying to understand what she's writing on the right side of the page. Looks like 1.5 on the top-right and 1-x on the middle-right. 🤔 Not sure what she's showing there. Your way makes sense in my brain. I'm not crazy after all! Thanks!
I just looked at that and automatically got that x had to equal 0 through intuition. But it was interesting to see that we always just assume x != 0 when dividing! Never noticed that but it makes complete sense.
@@ndeleonn I'm 73. When I was in grade school math and english were taught very intensely. We understood that we needed those skills to get along in life. Today... I meet people who can't solve 13 x 7 without a calculator, don't know how many minutes in a quarter hour, and can't even work out simple sentences. Education is NOT what it used to be.
Went straight to the comments section to see how everyone got to zero. I knew it intuitively just by looking at the equation. Love the linear algebra proofs. Would’ve taken me awhile to get to that. If ever!
I can’t believe I’d never been taught this trick before. It’s so obvious once you hear it that graphing both sides would produce all the solutions wherever the graphs intersect Thank you!
Infinity usually doesn't count here because it's a concept and not a number. There may be situations where that's an acceptable answer to this, but we're normally not looking for trivial answers and infinity when we're solving things like this.
It's not correct. If you put ○○ for x it will only bring you to ○○ = ○○/5 and this means ○○ = ○○ , which may be right but it's not a solution for this equation. The only solution for 4x = 0 is x = 0 I don't even believe that ○○ equals ○○/5 because it doesn't make sense. Any number devided by 5 can never equal this number, except 0.
Excellent. Straight forward diving into the solution and elucidating an important concept. Unlike some other channels that I guess are aiming for long videos to satisfy the UA-cam algorithm?
If you go the division route, as soon as you get 5=1 that should tip you off that you divided by zero somewhere. (All those gag mathematical "proofs" showing 1=2 depend on dividing by zero.) And since the only thing you divided by was x, then x must be 0. Then you can go back and do it right.
Yes, or it's a broken problem, but either way it's worth taking a bit to consider what's going on because that's not an acceptable result. In general when you have a step where all the variables disappear, you have to take a step back and consider what's happening. Often it's a mistake, sometimes it's the result of there just not being a solution, for example, looking for where Y=5x crosses Y = 5x +1. They're parallel, and won't cross without freaky curved surfaces. Or, if we're in 3, or more, dimensions, they could be skewed.
There are actually two solutions: x = 0 and x = infinity, because 5.0 = 0 and 5.infinity = infinity. So both for 0 and infinity the statement 5x = x is a true statement
@@Cruz8R Rubbish. The mathematics of transfinite numbers is an entire field of study in its own right. The first infinity is called aleph-null, N(0), (it is actually.a Hebrew letter and (0) is a subscript but UA-cam text cannot handle either). Here are some baby-steps for you: N(0) plus any finite number equals N(0) N(0) times any finite number equals N(0) Now go and find out how aleph-1 is produced (perhaps you should have researched that first before commenting on a topic that you do not understand).
@@Cruz8R That is debatable. The question is to solve the equation, not to solve the equation by inserting a number. And Infinity is a sign, like 1,2, X or Y than can appear in equation. Such as 1/0 = (infinity). So that makes infinity a valid answer to the question.
what i did was multiply everyone by 5 so 5X=X, then i remembered that there is one number that always equals itself regardless of what you multiply it with, 0 and if you divide 0 by something, the answer is always 0 so swapping X for 0 and we see that 5*0=0 as does 0=0/5.
All very neat and well explained. Though to me the real lesson of this is that it is an example of trying to solve a stupid equation, and people often do this when they don't think what it means. How can something be the same as one fifth of its value? So solving it is interesting, but realising what the equation means is perhaps more important!
I like the limit as x goes to infinity. So, x get bigger, and bigger, and bigger. But never getting really any closer to infinity. But it still grows ( instantaneously ) if we take smaller, and smaller, and smaller steps in time. Of course this must only be a thought experiment. Why should we only let Einstein experiment in his mind ? Well, there really were many other people doing thought experiments. Before they put their ideas on paper ( with some form of writing instrument ). I started this comment before seeing the video through the realistic solution. Of course, ... anything divided into zero is zero, ( except zero, which is not allowed. ) This professor is correct ! There, I admit it. All we have to do is go back to the beginning of our Algebra I class. Put the equation into standard form. Zero on the right hand side. Then divide it by 4. Again, though, one can easily solve this by inspection. ( X / 5 ) = 0 only when X = 0 QED, as my Algebra teacher would say. But, he wouldn't have allowed inspection. You know, steps and all.
Dividing by X (different than zero though), then and only then do you get to 5=1, which is impossible. Then X equals to the only value that we excluded in the earlier reasoning. So the equation is true only if X=0
Don't forget to check the answer! Suppose x is a solution. If x is not zero, we can divide by x to obtain 1=1/5, a contradiction. We deduce: if x is a solution then x=0. Now substitute x=0 back into the equation to show x=0 actually is a solution.
If 5x = x, then y=5x and y=x are true expressions. From the expressions, a graph of y=5x has a gradient of 5 and passes through the point 0,0. Similarly, a graph of y = x, has a gradient of 1 and passes through the point 0,0 Where both graphs meet, gives us the value of x, i.e. zero
i had a prof who would describe these types of 'solutions'' with phrasing like "5 equals 1 for small values of 5 … or large values of 1" to get us to check that our answer matches the question.
Countable infinity and I believe any version of uncountable infinity would also work. Some would say "hey, that's not a number" but then we wouldn't be able to speak of the cardinality of such sets... 🤣
Dividing both sides by x would be fine as long as you stipulate different cases. You have case 1 (x=0) and case 2 (x not 0). Case 1 substitute x=0 and the equation is correct therefore x=0 is a solution. Case 2 you can divide both sides by x, and it proves that there's no solution where x is not zero (works like proof by contradiction).
y'know...I didn't really think of how to do it algebraically. I was thinking to myself, how can you perform any operation on a number, and get the same number back? At first, I thought, this is an unsolvable equation, until...wait a minute, zero divided by anything is still zero. Plug in zero, yep! it works! So I just used the guessing method, which is not so reliable, but it worked this time.
Cross multiply which leaves 5x = x. Set the equation equal to zero by subtracting x from both sides leaving 4x = 0. Divide both sides by 4 and the result is x = 0. First semester algebra. 😉
I am 70 years old, do you know how many times I have used that in my life? NEVER! On the other hand I can fix almost any plumbing problem, most car problems,(recently a neighbor's VW had a problem the shop wanted 1200 to fix, I did it for 150 price of the part, and free labor) fix the stove, paint around the house, replace door locks, fix the vacuum cleaner, change a tire (you'll be surprised how many people can't) use an OBD to diagnose car problems, fix furniture, cook a little, sprinkler systems, simple electrical chores, like installing a ceiling fan they charge 100 bucks to do it light switches, and a pretty good disco dancer back im my day😊 According to my late math teacher Mr Wlock I was a good math student, at least that's what he wrote in my year book.
People keep trying to tell me that "infinity" is not an answer because either infinity is not a number or because they think that an arithmetical operation like addition or multiplication would not be allowed on infinity. Both are UNTRUE. As I will show. To start of with: Nobody asked for a number, what was asked was a *solution* . And x = infinity is a solution because 5.infinity = infinity is a TRUE statement. Which is also simple to show, as follows: - A common way to construct infinity is to make a series of numbers that never stops like so: x1 + x2 + x3 + ...... + xn, where n goed to infinity (∞) (such a series is called "countable infinite") - Now take the series and move each of the x's one position and put the same number in between again, so you get the series x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn. Which is also countably infinite if n -> ∞. - But x1 + x1 is the same thing as 2.x1 and 2.x1 + 2.x2 = 2.(x1 + x2) - In the same way, in the series that we just constructed x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn we have each term 2 times, so we may write: x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn = 2.(x1 + x2 + x3 + ...... + xn), which is equal to 2.infinity, because we already knew that (x1 + x2 + x3 + ...... + xn) is infinite if n -> ∞ - But we started by showing that x1 + x2 + x3 + ...... + xn = countably infinite, and we just saw that x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn is countably infinite if n -> ∞, and therefore that 2.(x1 + x2 + x3 + ...... + xn) if n -> ∞. - So we now know that both x1 + x2 + x3 + ...... + xn AND 2.(x1 + x2 + x3 + ...... + xn) are both countably infinite, which means that the statement 2.infinity = infinity is TRUE. - This mechanism works for any number a that (such as 5) that you want to put in the place where we used the number 2 (but it would be a bit to much to write out here). - Comparable mechanisms also work for other "non-countable" definitions of infinity but these are a bit to much work to explain / show here. *Conclusions:* A.) Basic arithmetical operations like addition, subtraction, multiplication and division are allowed on infinity, and are actually quite important (!) in Math ! For instance for Cantor's famous "diagonal proof" . B.) 5.infinity = infinity or infinity = infinity / 5 are TRUE statements and therefore infinity is a SOLUTION of the equation, as long as it is not specified that the solution must be a NUMBER. PS. If you want a nice animated illustration of what I just explained, look for a video on UA-cam from Veritasium, about Hilberts Hotel.
X=x/5 subtract x from both sides 0=x/5-x distributive property 0=x(1/5-1) Solve the parenthesis 0=x(-4/5) Multiply both sides by 5 and divide both sides by -4 0=x Solved.
I love math, I’m 52, algebra is my favorite by far, so this is fun fun fun!! I, however, haven’t ever heard my gears actually grind. Not even in college. Haha. I’m getting old. 🎉😂
I think the misstep in the red method is assuming x/x = 1. My algebra isn't qualified but this seems like a handy technique to solve specific equations but not a rule of math. Something about pulling a number out of a relationship involving only variable(s) isn't sitting right with me, but ya no math degree.
Thank you for the concise explanation. I also watch TabletClass Math, but his explanations are long and convoluted. I wish he would just solve the problem, instead of re-explaining algebra in every video.
It’s often useful to get students to make the entire equation = 0 as an habit, and then factor. So x(5 - 1) = 0 hence 4x = 0 so x = 0 being the only valid solution.
Yes. x = x/5 , _let us assume_ that x != 0 and divide both sides by x (otherwise we couldn't). That gives us: 1 = 1/5 But that's false, marking a contradiction with _some_ of our assumptions. We've made only one: that x != 0. Therefore, x = 0, QED.
But it's clear from the beginning that x == 0. x is on both sides of the equation and there are no additions or subtractions, AND x is on top of the fraction. x == 0 where x is alone on one side, and x has only a multiplier or a divisor on the other. If the equation were x = x divided by the square root of -1 it would still be 0.
Zero to the left of me, zero to right, here I am stuck in the middle with nowt, nought, nada. Bah, I need a hug, or a one, anything but a zero! Lovely video to help me make nothing out of nowt and vice versa. My edentate granny would have been proud of me. I think...
The process seems to me like creating a solution for the equation rather that actually solving the equation. In other words manipulating the expressions with arbitrary computations until a solution - any solution - is able to be produced.
5x = x iff 5x-x=4x iff 4x = 0 The quadratic equation Ax^2 + Bx + c = 0 has no solution for x = 0. A.B.C real natural numbers except c = x = 0. 5x - x = 0 iff x 5 = 1 0r x = 0 A = 0 B = 5x-x = 4x The quadratic equation becomes 4x + c = 0 4x = -c There are no negative numbers: -c = a - 4x. 4x > a iff 4x-c = a (Imaginary numbers are complex only for those who think they are somehow real; SU(2) is much ado about nothing. (Note that if there are no negative numbers, thre are no square roots of negative numbers (i.e., imaginary numbers) Bottom Line Pythagoras was wrong, Fermat was correct even for n = 2 Proof of Fermat's Last Theorem c^n a^n + b^n for n > 1 (and therefore for n > 2. c:= a + b (addition, "existence" group under addition c^n = (a+b)^n = [a^n + b^n] + f(a,b,n) (Binomial Expansion) c^n = [a^n + b^n] iff f(a,b,n) = 0 f(a,b,n) 0 c^n [a^n + b^n] QED This result has profound consequences for the Standard Model of Theoretical Physics, not to mention Foundation of Mathematics, but I don't have the spacetime to write it here. I publish on the physicsdiscussionforum dot org for those interested.
@MathQueenSusanne no, but it crops up from time to time in various projects. Just knowing this little fact is sure to reduce my frustration when it does. Thank you for your efforts and enthusiasm.
Hey math friends! If you’re enjoying this video, could you double-check that you’ve liked it and subscribed to the channel? It’s a simple equation: your support + my passion = more great content! Thanks for helping me keep this going - you’re the best!
Ohhh, you speak English!🤗
I was curious. So, if we rearrange thi equation, we get 5 =x/x
And if we substitute the solution- the value of x = 0, it should be satisfied. Right?
What do they call equations whose variable values satisfy them and also do not satisfy them?
@@Dreosaurus Thanks, I understand. But that was my point since x=0 is the solution, why does it not hold when the equation is re-written in the other form?
5?
I am 67 and always had a keen interest in math in the sense that math is a numerical form of measurement of the physical world in which we live. Although, I love math I was never really all that good at it. Well, in high school I got by. Perhaps I am just very rusty at it now after all of these years. And that is where you and your wonderful channel comes in. Thank you, Math Queen, for helping me in my journey of kicking the mathematical rust off.
This is demonstrating the classic pitfall of dividing by an unknown value where that value could be zero. Mathematical fallacies where starting with an equation and going through a list of apparently logical steps results in something like 2=1 often involves dividing by zero at one step.
dividing by zero WILL NOT MAKE TIME/SPACE STOP - THAT IS A LIE MATH NERDS TELL PEOPLE SO THEY WILL BE AFRAID TO DO MATH
Susanne, your solution is mathematically convincing. However, the fact that only zero fits is actually evident at first glance because one-fifth of x can never be x, except when x is zero.
While it is evident (provided your numeracy skill is sufficient to deduce that) you haven't solved the equation. To solve the equation you need to do what she did, which is get x on its own on one side and a value on the other. Knowing the answer != solving the problem.
That's not the point of this channel. It's not about mathematical rocket science, but rather about making it accessible to an average high school student.
It's more than convincing. Your approach could be to factor out x. x•1 = x•(1/5). That is x(1=1/5), (making "sense" only for x=0) or more systematically -- like in the video; x(1-(1/5)) = 0, x(4/5) = 0, x = (5•0)/4 = 0. It's important to work up a number sense like you have done. But it's also vital to learn to be formal. Then one can communicate knowledge better and also interpret knowledge better.
Doesn't ∞ work ?
@@WideCuriosity Infinity works. But infinity is not a number.
x=5x then draw the the two lines (y=x) and (y=5x). They meet only in point (0,0). So x=0
Kind of an odd way
This way makes much more sense than picking up a 1 seemingly out of thin air.
@@Coolmoed graphical solutions help sometimes because one can literally visualize just how verified the solution is... It's just another tool that some people prefer.
@ if needed pictures can be great
Not when it makes more work tho
@@Coolmoed more work is absolutely welcome if it helps something stick for someone. It's not always about getting the answer just to say you did. Some students actually care about gaining a deeper understanding of the overall, which includes reconciling across multiple methods sometimes.
At first i thought, you are looking for the answer 0.. But the value of your video is the HOW we get there. Well done.
You needed 4 minutes of explanation to understand how to solve 4/5 x = 0?
trial solutionis:: sometimes very good
As a communications and electronics engineer grad and math enthusiast for years, I can wholeheartedly say that this channel was sth I absolutely NEEDED to see.
It helped me remember after such a long time what the applying the basics actually looked like, using the most basic of steps instead of just the advanced type I'm already used to reminded me of the insights doing more basic steps gets me.
I thank you from the bottom of my heart for once again reminding me of the beauty of even the simplest and most basic parts of maths.
Chuck Norris divides by zero.
🤣
Is chuck norris a solution in R?
I got the Chuck Norris add-in for Excel. Instead of #DIV/0! I got #WHENIWANTYOUROPINIONILLBEATITOUTOFYOU!
Whe know that event as the "big bang"
@@drunkenstyle7899 can’t be, Chuck Norris is even a statistical anomaly 😏
One other number that works is infinity because infinity is equal to infinity/5. its the same concept as dividing by 0 because any number divided by 0 is infinity. This answer is as valid as x=0.
That was the conclusion I came to - I haven't watched the video, but I multiplied each side by 5, then it has to be x = 0, or x = infinity, since 5 * infinity = infinity. Prove me wrong, somebody!
This was actually a nice little exercise when you haven’t been doing “school maths” for years. Nice brush-up!
Awesome, that you tried it again after so many years!
And there's not only those who haven't done it in a while. There are also those of us who weren't very good at it to begin with! HAHA! :)
As an engineer I knew it was zero but did the work to see why. But I agree...Kids in the USA are behind in math for many reasons and memorization is one of them
Simple, but enjoyable. I liked the point about dividing by zero warning.
I've just come across your channel in the last few days, I'm 56 now and it's nice to pause your video at the start and then try and work your sums out. Also to look at how you solve them.
Thanks for demonstrating what happens if you try and cancel out x when you don't know what it is.
For my part I'd figured if you solve for x then the last thing you want to do is cancel x out of the equation. and once you remember that 0 divided by anything = 0 the equation becomes very easy to solve.
Love the contrasting solution attempts. It's always good to remind oneself that when you divide by the variable x, you need to exclude the x=0 solution. But that doesn't mean you don't check to see if x=0 is a solution, which in this case would immediately show that it's a solution. That said, as a retired math teacher, I really appreciate that you point out that both x and x/5 are linear functions, so to collect the like terms on one side. Voilá! Thanks!
This may all seem very dumb, but it goes to demonstrate that blindly applying rules and techniques won't necessarily solve every math problem. And yet this is what kids learn at school: blindly throwing out memorized rules instead of pausing for a moment and actually thinking.
Disagree; the solution is to use a BETTER set of memorized rules and apply them blindly. The better rule, in this case, is to put everything on one side and factor, and not cancel variables out.
@kingbeauregard I'm not sure if you're being ironic, or if you're just as dumb as a mule.
Wonderful. I saw x=0 immediately but I was wondering if there could be another solution in complex numbers. You showed convincingly that 0 is the only solution.
No! x=infinity also is a solution!!
There can only be one solution because the equation is linear. You can easily identify a linear equation when the power of x is 1.
@@paulbowler2760 It is not. The equation is linear (a straight line). If you were to graph it, it would hit the x-axis once and exactly once.
@@paulbowler2760 No, it isn't. Infinity is not a number and thus not a valid solution for this equation.
@@paulbowler2760 I think so too.
I actually paused the video trying to figure out the right answer, but couldn’t find it. I think I was so stuck in the thought of not understanding an equation could be “impossible”. Thanks Math queen for learning me this!:)
x=0. took 0.5 seconds
Did you time it? lol
.2
This isn't for you.
I got infinity. Took me one tenth of a second.
@@EastWindCommunity1973 you got it wrong
X= X/5
therefore (subtracting X/5 from both sides)
4X/5 = 0
therefore (multiplying both sides by 5)
4X = 0
therefore (dividing both sides by 4)
X=0
QED
You can prove absurdities by dividing by zero.
True, but in this case it is zero divided by a non-zero number.
That made me happy. I was like, "Does not compute" but once I realized it was 0 all was well in the world again.
I just got an expression 5x=x and was like "0 is the only number that can be multiplied by a constant and remain itself, therefore the answer is 0" but then I understood that its not a "solution" technically and I "guessed" the answer. Was actually curious how to *solve* solve it. Been years since I subtracted from equations lol
Awesome, that you’ve been so curious, although you found the answer by yourself already!
"Been years since I subtracted from equations lol"
I see what you did there ^^
I did the same mental logic, except I applied it to x=(1/5)x so I didn't have to multiply both sides by 5 first :p
The answer is 0.
Wish I'd had a math teacher like her. I'd have paid a lot more attention.
"We're never gonna use this stuff!" If you think this know that I use math and algebra regularly for finance and in my job, mostly involving electrical/electronic calculations. Basic algebra makes it easy to calculate your range in a car, boat, or aircraft. I used trig and algebra to figure out how many boards to buy and at what angles and lengths to cut the rafters for a shed I built. It cost maybe 20% for me to build it rather than pay others to do it for me. It also feels great to build things. Every cool thing we have is built on math.
THAT IS JUST A RELITAVE PERSPECTIVE - ITS JUST AS LIKELY - THAT MATH IS BUILT ON COOL STUFF _JUST SAYING
@HNH421 I've been interested in math all my life, and trust me, math is built on the weirdest stuff imaginable! It's a good thing I think weird stuff is cool. :)
@@eekee6034 i hate maths - its the way they flutter around light bulbs, i also hate being quonicly bislexic : (
@HNH421 Some investigation might be required. You might find that math was originally deemed to be philosophy.
@@randyduncan795 I am of the opinion, that most philosophy is Sophistry, referring to its use, of fallacious arguments, misleading language, and rhetorical tricks to deceive or manipulate others. but I do not believe in other people, because I am a solipsist, a philosophical idea that suggests one’s own mind is the only true reality, and that all other people and external objects are mere creations or projections of my own mind. So the question remains why am I replying to my Self in this comment section ? The answer is because I am a somnambulist that is asleep.
Thank you! I've been falling in that pit for 30+ years and never knew *why* it happened. Now I do, that's going to make everything easier. Brilliantly explained.
You truly draw this out
The division by x route is actually very fast. Any time you divide (or multiply by the inverse) you must check that an inverse exists. In other words, you check to see if x = 0 is a valid solution. It is valid so no further algebra is needed.
Wow! The Math Queen is a knockout. I've never seen math look this beautiful before.
At first I thought 'How does she spin out this easy equation for a 4 minute video?' but when I actually watched it, your approach of showing the wrong way to tackle it makes sense educationally. Division by zero errors are very important to avoid!
It’s nice watching you solve the problem! I really like your voice!
Thank you so much for your kind words and welcome to my channel!
Dividing by x is in many cases the only to procede so you must know how to do this properly, i.e treating the case x=0 seperately. It’s really a special of the very useful zero product rule
Let's take a moment and remember or recognize this woman has one of the most wonderfull singing voices in the universe!😊
Mradam you are perfectly correct
1x cannot be equal to 1/2 x
Like saying 1= 1/2
Not a good question
I wouldn’t be able to learn math with this cutie teaching
Same here-I gave up and enjoyed the view. Brains and beauty all wrapped into one.
You would if you went to school
@
No joking around allowed here… got it
Another way is with geometry, x=x/5 means finding all the x-es where the two curves have the same y, y=x and y=x*1/5, so the only x where they have the same y is x=0.
The greatness of dividing by 0 : If you divide by a Zero, you create an absurd answer. Great choice of video ^^
-Early secondary school : x = x/5, x - x/5 = 0, x.(1-1/5) = 0 as (1-1/5)>0 then x = 0
-Middle secondary school : where f(x) = x crossing with f(x) = x/5 ? Only when x = 0
You can devide by x. But if you do you have to check if x=0 is a solution first, because you aren't allowed to divide by 0.
I first thought that it would have no solution since I didn't think of the case where x is zero. Very informative video.
This must be the prettiest math teacher.
I'd have like to seen the generalization that dividing b y the variable is a bad idea not just "if you don't know what you're doing," but rather especially if you might be dividing by zero because yes, that's when you get "solutions" like 1 = 5.
5x = x
5x - x = 0
4x = 0
x = 0
😊
Another approach:
5x - x = 0
x(5-1) = 0
from here it's either x=0 or 4=0, as 4 most certainly can't be 0 so it must be that x=0
Yep, those are also good ways to go about it.
@@SmallSpoonBrigadethank you! I'm sitting here going crazy trying to understand what she's writing on the right side of the page. Looks like 1.5 on the top-right and 1-x on the middle-right. 🤔 Not sure what she's showing there. Your way makes sense in my brain. I'm not crazy after all! Thanks!
I just looked at that and automatically got that x had to equal 0 through intuition. But it was interesting to see that we always just assume x != 0 when dividing! Never noticed that but it makes complete sense.
I'm 70 and I still saw that solution immediately.
I still remember my math teacher in about 4th grade telling me that the only value that can be both itself and itself divided by something is 0 (zero)
65 here, and I saw it right away as well.
It’s awesome, that you all keep on training your brain and that we have people of all ages here on my channel!
What does age have to do with "seeing' the solution?
@@ndeleonn
I'm 73. When I was in grade school math and english were taught very intensely. We understood that we needed those skills to get along in life.
Today... I meet people who can't solve 13 x 7 without a calculator, don't know how many minutes in a quarter hour, and can't even work out simple sentences.
Education is NOT what it used to be.
Went straight to the comments section to see how everyone got to zero.
I knew it intuitively just by looking at the equation. Love the linear algebra proofs. Would’ve taken me awhile to get to that. If ever!
A simpler way: draw graphs
y = x
y = x/5
I can’t believe I’d never been taught this trick before. It’s so obvious once you hear it that graphing both sides would produce all the solutions wherever the graphs intersect
Thank you!
Yeah, that’s also a nice way! Thanks for sharing!
The 1-x throw me off. I when I write it as -x on each side, that makes more sense.
I think there are three solutions: +infinity, - infinity, zero
this is the correct answer
Infinity usually doesn't count here because it's a concept and not a number. There may be situations where that's an acceptable answer to this, but we're normally not looking for trivial answers and infinity when we're solving things like this.
It's not correct. If you put ○○ for x it will only bring you to ○○ = ○○/5 and this means ○○ = ○○ , which may be right but it's not a solution for this equation. The only solution for 4x = 0 is x = 0
I don't even believe that ○○ equals ○○/5 because it doesn't make sense. Any number devided by 5 can never equal this number, except 0.
Excellent. Straight forward diving into the solution and elucidating an important concept. Unlike some other channels that I guess are aiming for long videos to satisfy the UA-cam algorithm?
x=x/5 x=0 It’s in my head.
If you go the division route, as soon as you get 5=1 that should tip you off that you divided by zero somewhere. (All those gag mathematical "proofs" showing 1=2 depend on dividing by zero.) And since the only thing you divided by was x, then x must be 0. Then you can go back and do it right.
Yes, or it's a broken problem, but either way it's worth taking a bit to consider what's going on because that's not an acceptable result. In general when you have a step where all the variables disappear, you have to take a step back and consider what's happening. Often it's a mistake, sometimes it's the result of there just not being a solution, for example, looking for where Y=5x crosses Y = 5x +1. They're parallel, and won't cross without freaky curved surfaces. Or, if we're in 3, or more, dimensions, they could be skewed.
There are actually two solutions: x = 0 and x = infinity, because 5.0 = 0 and 5.infinity = infinity. So both for 0 and infinity the statement 5x = x is a true statement
Some Queen, eh? Should have said 'aleph-null' is also a solution, and really baffled her!
Infinity is not a number but a concept. So infinity is not a solution.
@@Cruz8R Rubbish. The mathematics of transfinite numbers is an entire field of study in its own right. The first infinity is called aleph-null, N(0), (it is actually.a Hebrew letter and (0) is a subscript but UA-cam text cannot handle either). Here are some baby-steps for you:
N(0) plus any finite number equals N(0)
N(0) times any finite number equals N(0)
Now go and find out how aleph-1 is produced (perhaps you should have researched that first before commenting on a topic that you do not understand).
@@Cruz8R That is debatable. The question is to solve the equation, not to solve the equation by inserting a number. And Infinity is a sign, like 1,2, X or Y than can appear in equation. Such as 1/0 = (infinity). So that makes infinity a valid answer to the question.
@@DJF1947 Or any aleph number for that matter...
what i did was multiply everyone by 5 so 5X=X,
then i remembered that there is one number that always equals itself regardless of what you multiply it with, 0 and if you divide 0 by something, the answer is always 0
so swapping X for 0 and we see that 5*0=0 as does 0=0/5.
0 divided by any number is 0.
Correction: 0 divided by any number not equal to 0 is 0
Any number divided by zero (except zero) is _undefined_ .
Zero divided by zero is _indeterminate_ .
I enojoyed your performance, more than the solution, because it was obvious, X have to be ZERO. You did it nicely.
x may also be infinity. (notice that it was not said that x needs to be a number!)
All very neat and well explained. Though to me the real lesson of this is that it is an example of trying to solve a stupid equation, and people often do this when they don't think what it means. How can something be the same as one fifth of its value? So solving it is interesting, but realising what the equation means is perhaps more important!
DUH!!!! That took me waaaay too long to figure out. Well done.
I like the limit as x goes to infinity. So, x get bigger, and bigger, and bigger. But never getting really any closer to infinity. But it still grows ( instantaneously ) if we take smaller, and smaller, and smaller steps in time.
Of course this must only be a thought experiment. Why should we only let Einstein experiment in his mind ?
Well, there really were many other people doing thought experiments. Before they put their ideas on paper ( with some form of writing instrument ).
I started this comment before seeing the video through the realistic solution. Of course, ... anything divided into zero is zero, ( except zero, which is not allowed. )
This professor is correct ! There, I admit it. All we have to do is go back to the beginning of our Algebra I class.
Put the equation into standard form. Zero on the right hand side. Then divide it by 4.
Again, though, one can easily solve this by inspection.
( X / 5 ) = 0 only when X = 0
QED, as my Algebra teacher would say.
But, he wouldn't have allowed inspection. You know, steps and all.
Dividing by X (different than zero though), then and only then do you get to 5=1, which is impossible. Then X equals to the only value that we excluded in the earlier reasoning. So the equation is true only if X=0
The key to understanding this is knowing the difference between undefined and indeterminate
So, for me, the way to enjoy math is to combine it with other things passionate about.
Don't forget to check the answer! Suppose x is a solution. If x is not zero, we can divide by x to obtain 1=1/5, a contradiction. We deduce: if x is a solution then x=0. Now substitute x=0 back into the equation to show x=0 actually is a solution.
If 5x = x, then y=5x and y=x are true expressions.
From the expressions, a graph of y=5x has a gradient of 5 and passes through the point 0,0.
Similarly, a graph of y = x, has a gradient of 1 and passes through the point 0,0
Where both graphs meet, gives us the value of x, i.e. zero
i had a prof who would describe these types of 'solutions'' with phrasing like "5 equals 1 for small values of 5 … or large values of 1" to get us to check that our answer matches the question.
Sounds like the math behind Intel's first Pentium processor.
@@javaman7199 _It's all about the Pentiums, Baby_ 😆you've outed yourself, mr. greybeard ¬ time to upgrade too a DX and hit that 'turbo switch'
I learned why we can’t divide by an unknown during solving equations, thank you
Countable infinity and I believe any version of uncountable infinity would also work. Some would say "hey, that's not a number" but then we wouldn't be able to speak of the cardinality of such sets... 🤣
Dividing both sides by x would be fine as long as you stipulate different cases. You have case 1 (x=0) and case 2 (x not 0). Case 1 substitute x=0 and the equation is correct therefore x=0 is a solution. Case 2 you can divide both sides by x, and it proves that there's no solution where x is not zero (works like proof by contradiction).
A bit middle school math in the morning. Nice😊
Haven't done this in awhile. Thanks for the explanation.
That was an elegant solution. Liked and Subscribed.
Thank you so much for your kind words and for subscribing! That makes me happy!
Beautiful teacher!
y'know...I didn't really think of how to do it algebraically. I was thinking to myself, how can you perform any operation on a number, and get the same number back? At first, I thought, this is an unsolvable equation, until...wait a minute, zero divided by anything is still zero. Plug in zero, yep! it works! So I just used the guessing method, which is not so reliable, but it worked this time.
Cross multiply which leaves 5x = x. Set the equation equal to zero by subtracting x from both sides leaving 4x = 0. Divide both sides by 4 and the result is x = 0. First semester algebra. 😉
I am 70 years old, do you know how many times I have used that in my life? NEVER! On the other hand I can fix almost any plumbing problem, most car problems,(recently a neighbor's VW had a problem the shop wanted 1200 to fix, I did it for 150 price of the part, and free labor) fix the stove, paint around the house, replace door locks, fix the vacuum cleaner, change a tire (you'll be surprised how many people can't) use an OBD to diagnose car problems, fix furniture, cook a little, sprinkler systems, simple electrical chores, like installing a ceiling fan they charge 100 bucks to do it light switches, and a pretty good disco dancer back im my day😊
According to my late math teacher Mr Wlock I was a good math student, at least that's what he wrote in my year book.
It's solved right off the bat.... Only a Susan would convolute that...
People keep trying to tell me that "infinity" is not an answer because either infinity is not a number or because they think that an arithmetical operation like addition or multiplication would not be allowed on infinity. Both are UNTRUE. As I will show.
To start of with: Nobody asked for a number, what was asked was a *solution* . And x = infinity is a solution because 5.infinity = infinity is a TRUE statement. Which is also simple to show, as follows:
- A common way to construct infinity is to make a series of numbers that never stops like so: x1 + x2 + x3 + ...... + xn, where n goed to infinity (∞) (such a series is called "countable infinite")
- Now take the series and move each of the x's one position and put the same number in between again, so you get the series x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn. Which is also countably infinite if n -> ∞.
- But x1 + x1 is the same thing as 2.x1 and 2.x1 + 2.x2 = 2.(x1 + x2)
- In the same way, in the series that we just constructed x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn we have each term 2 times, so we may write:
x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn = 2.(x1 + x2 + x3 + ...... + xn), which is equal to 2.infinity, because we already knew that (x1 + x2 + x3 + ...... + xn) is infinite if n -> ∞
- But we started by showing that x1 + x2 + x3 + ...... + xn = countably infinite, and we just saw that x1 + x1 + x2 + x2 + x3 + x3 ...... + xn + xn is countably infinite if n -> ∞, and therefore that 2.(x1 + x2 + x3 + ...... + xn) if n -> ∞.
- So we now know that both x1 + x2 + x3 + ...... + xn AND 2.(x1 + x2 + x3 + ...... + xn) are both countably infinite, which means that the statement 2.infinity = infinity is TRUE.
- This mechanism works for any number a that (such as 5) that you want to put in the place where we used the number 2 (but it would be a bit to much to write out here).
- Comparable mechanisms also work for other "non-countable" definitions of infinity but these are a bit to much work to explain / show here.
*Conclusions:*
A.) Basic arithmetical operations like addition, subtraction, multiplication and division are allowed on infinity, and are actually quite important (!) in Math ! For instance for Cantor's famous "diagonal proof" .
B.) 5.infinity = infinity or infinity = infinity / 5 are TRUE statements and therefore infinity is a SOLUTION of the equation, as long as it is not specified that the solution must be a NUMBER.
PS. If you want a nice animated illustration of what I just explained, look for a video on UA-cam from Veritasium, about Hilberts Hotel.
X=x/5
subtract x from both sides
0=x/5-x
distributive property
0=x(1/5-1)
Solve the parenthesis
0=x(-4/5)
Multiply both sides by 5 and divide both sides by -4
0=x
Solved.
I love math, I’m 52, algebra is my favorite by far, so this is fun fun fun!! I, however, haven’t ever heard my gears actually grind. Not even in college. Haha. I’m getting old. 🎉😂
I saw zero as the only solution but I like the way you resolved it.
infinity, or rather infinite amount of infinities (there are really many) are also solutions. This is absurd, not equation
To get all the solutions, always factor, don't cancel things out. It's a reliable rule of thumb.
I think the misstep in the red method is assuming x/x = 1. My algebra isn't qualified but this seems like a handy technique to solve specific equations but not a rule of math. Something about pulling a number out of a relationship involving only variable(s) isn't sitting right with me, but ya no math degree.
it's 0. the larger, or smaller you get from 0, the larger/smaller the difference becomes between the left and right sides of that equation.
My way of looking at this is 5x=x so if you divide both sides by x you get 5=1
Thank you for the concise explanation. I also watch TabletClass Math, but his explanations are long and convoluted. I wish he would just solve the problem, instead of re-explaining algebra in every video.
It’s often useful to get students to make the entire equation = 0 as an habit, and then factor. So x(5 - 1) = 0 hence 4x = 0 so x = 0 being the only valid solution.
Yes.
x = x/5 , _let us assume_ that x != 0 and divide both sides by x (otherwise we couldn't). That gives us:
1 = 1/5
But that's false, marking a contradiction with _some_ of our assumptions. We've made only one: that x != 0. Therefore, x = 0, QED.
Proof by "reductio ad absurdum". 👍
@ Time to time, it’s worth to remind oneself of the utter trivia of how mathematical logic works… ;-)
La misma lógica indica que es ZERO, excelente explicación, gracias.
As with life itself, the journey to reaching the goal is where the beauty lies.
if you divide by zero you create singularity and there 1=5
bcs 1*infinite = 5*infinite
But it's clear from the beginning that x == 0. x is on both sides of the equation and there are no additions or subtractions, AND x is on top of the fraction. x == 0 where x is alone on one side, and x has only a multiplier or a divisor on the other. If the equation were x = x divided by the square root of -1 it would still be 0.
Incredible maths
How would we demonstrate that the answer could be "infinite"? "Infinite" is a possible solution, right or no?
Zero to the left of me, zero to right, here I am stuck in the middle with nowt, nought, nada. Bah, I need a hug, or a one, anything but a zero! Lovely video to help me make nothing out of nowt and vice versa. My edentate granny would have been proud of me. I think...
5 = 1 . Amazing example why we can’t divide by 0 👌
Wow! Excellent video and explaination. I only clicked on the link because I was sure there was no solution. I have clicked Like and subscribed.
The process seems to me like creating a solution for the equation rather that actually solving the equation. In other words manipulating the expressions with arbitrary computations until a solution - any solution - is able to be produced.
Not really. There is only one solution.
*_Каноническое решение, супер корректное. Претензий не может быть. Super correct._*
5x = x iff 5x-x=4x iff 4x = 0
The quadratic equation Ax^2 + Bx + c = 0 has no solution for x = 0. A.B.C real natural numbers except c = x = 0.
5x - x = 0 iff x 5 = 1 0r x = 0
A = 0
B = 5x-x = 4x
The quadratic equation becomes 4x + c = 0
4x = -c
There are no negative numbers:
-c = a - 4x. 4x > a iff 4x-c = a
(Imaginary numbers are complex only for those who think they are somehow real; SU(2) is much ado about nothing.
(Note that if there are no negative numbers, thre are no square roots of negative numbers (i.e., imaginary numbers)
Bottom Line Pythagoras was wrong, Fermat was correct even for n = 2
Proof of Fermat's Last Theorem c^n a^n + b^n for n > 1 (and therefore for n > 2.
c:= a + b (addition, "existence" group under addition
c^n = (a+b)^n = [a^n + b^n] + f(a,b,n) (Binomial Expansion)
c^n = [a^n + b^n] iff f(a,b,n) = 0
f(a,b,n) 0
c^n [a^n + b^n] QED
This result has profound consequences for the Standard Model of Theoretical Physics, not to mention Foundation of Mathematics, but I don't have the spacetime to write it here. I publish on the physicsdiscussionforum dot org for those interested.
n+4=4^^4=[n3]
Multiply both sides by 5 to obtain 5X = X. X = 0
I love a maths equation! I've subscribed!
Awesome, thank you so much! I hope you enjoy my other videos as well.
Thanks
Wow, thank you soooo much for your generosity! All the best to you! Do you need math at the moment for some kind of exam?
@MathQueenSusanne no, but it crops up from time to time in various projects. Just knowing this little fact is sure to reduce my frustration when it does. Thank you for your efforts and enthusiasm.
That’s awesome, that I could reassure you. Then enjoy your upcoming projects!
x = x/5 , 5x = x
5x -- x = 0
x(5 --1) = 0
4x = 0
x = 0