The biggest MYTH in math 😳

99% of students and teachers still think this is true. Here's the truth instead.

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[dcoch]

I've never heard of a "shifting rule." I was taught to do just as you said; isolate X by subtracting from both sides.

[Kevin_Street]

This is how I was always taught. Or rather, I remember the teacher putting the minus threes (or plus threes or whatever) on either side of the equals sign, and we were supposed to intuitively understand what was happening without being told. A lot of algebra was like that: first a very brief, often unhelpful explanation, then a lot of problems solved in detail on the blackboard.

[Khalid-Ibn-Al-Walid]

This is really my favourite physics channel ! It explains things fundamentally and with pure logic ! Nothing is admitted, everything is about building step by step with pure logic without learning ! It's like the difference between learning how to build an house, or using pure logic and elementary "bricks" to try to build the house from scratch by ourselves !

[cambodianginger]

when I first started inequalities chapter in 11th I had log forgotten about this concept but inequalities taught it again to us

[Jrdan]

Wow, I didn't know that doing the same operation to both sides was taught like that. I feel like if I was taught that way I might have started to hate math.

[tonim.]

One of my math teachers tought us, to think of it as an "old" balancing scale, which has to be always balanced. Found that analogy quite helpful. Greetings to Herr (Mr.) Benner!

[darby]

Thank you for teaching the correct rule. The shifting "gimmick" worked on this very simple equation - but this is a physics oriented channel. Physics equations are rarely X+3 = 5 simple. You teach it right the first time and it saves the student frustration later on when the "gimmick" shortcut no longer works.

[amigalemming]

Actually in my case I invented the "shifting rules" by myself and later in school we were taught that in contrast to that, equational reasoning works like a balance. If you put or remove the same amount of weights to or from both sides then the balance will remain in equilibrium.
The general rule is, that if x=y then for any function f, it also holds f(x)=f(y). This is connected to the extensionality of functions.
When we are talking about addition, subtraction, multiplication and division then there is not much difference between the shifting rules and the balance metaphor. However, I had serious debates with mathematicians whether squaring or extracting the square root is allowed in equational reasoning. Of course it is. These are just special cases for f. However, people tend to combine application of f with subsequent simplifications that can be wrong. For instance: x²=25. Take square root on both sides yields sqrt(x²) = sqrt(25), and not x=5. It certainly holds sqrt(25) = 5, but sqrt(x²) is not equal to x, but to |x|.

[igor]

Started teaching my 5yo equations, and started right with subtracting/adding things on both sides, my wife was passing by and said - just tell him about shifting, but I’ve declined it as this is not how the maths works, and 3 days after i see this video

[mathemitnullplan]

so true! it becomes even more clear if you add a bar right to the equation and write down what you want to do with both sides.

[fernandocacciola]

Ok this was really but really good because I was, say, "ill-conditioned", to shift around as you said. So even though I know and do it "the right way" many times with far more complex equations, I've never noticed how the shifting is really an *unnecessary* oversimplification of the actual correct procedure until you said it!
Now this is really important because when I was trying to teach my kid to "shift around", he would often forget to "invert" the sign or the operation, because as you said, that was just an arbitrary rule he had to just memorize, but couldn't. Had I taught him the correct procedure right from the start, he would have not struggled at all!!

[soniacz]

Im autistic and I’ve been teached the „shifting” method. I remember how I was struggling with this bc it wasn’t intuitive, I needed to remember that and I was like “but WHY?!”, like I was missing an important piece of information. Now it makes perfect sense! It’s logical. It’s obvious. Years after my teacher firstly introduced equations in math class… I hate “it is what it is, just accept it”, it need to be logical for me.

[KorraTransPhoenix]

I was never taught this "shifting rule" in school. This is the first I'm hearing about it. I was tought to always balance the equation. If you do something on one side, do it on both sides. Always. This other method does sound pretty devoid of learning, ironically.

[abhshk]

that's why this rule doesn't applicable in solving inequalities

[neilatkins]

Actually you have to do it as
X + 3 = 5
(X + 3) + -3 = 5 + -3
X + (3 + -3) = 2 associative law
X + 0 = 2 summation of inverses
X = 2 identity law

There are no laws for subtraction and division. They are shorthand for addition and multiplication of inverses. So (x - 1) - 2 is not equal to x - (1 - 2) but (x + -1) + -2 = x + (-1 + -2). This is really key to understand what is happening.

[academyofuselessideas]

your explanation is exactly how i was taught about it. In general, the equal sign is telling you that whatever is in the right and whatever is in the left are two representations of the same number. So, applying any function to both sides respects equality... in symbols if x=y then f(x) = f(y) for any function... However, here is what blew my mind: how different my life would've been if instead of explaining this to me, they had made me memorize all those other rules? 🤯

[zat]

That is so sad that this is skipped. Understanding the logic of methods are fundamental to greater literacy down the line.

I may use “shifting” to visualize mental math, but I was still taught the concept.

[ayushsharma]

In general functions preserve equality if you respect the domain, no manner what system

[name-nam]

finally, a video from you where i have discovered the lesson myself before!

[go_beyond_the_sky]

Sir, what is the wrong way?? Everyone knows and if you show subtraction it takes time, and you know that you have only 180 minutes to solve all 75 questions, ,, so don't think this is this is logical . It's useless to show this step.