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“I m going to talk about solving equations equations solving them now an equation in in this course is going to be something like this the left hand side equals right hand side talk about inequalities later. I guess. But the left hand side equals. The right hand side so the left hand side whether it is on the left.
It might be something like x. Squared. Plus. 4x.
Minus. 5y plus. 17. I don t know some complicated thing x.
To power. 5. And the right hand side might be equal to k..
Plus. 4. Minus. X.
Cubed. Plus. 17. Some complicated thing equals.
Some other complicated thing. And we want to find out what axis and sometimes we can do it and sometimes you can t when i write this down the left hand side equals. The right hand side. I can say that 2 times.
The left hand side equals 2 times the right hand side because i imagine i ve got my hands in front of me. And i ve got some thing a little bunch of some things in my left hand and i ve got something in my right hand and i m looking at them. And i say might be complicated..
I might not be able to understand it very well. But i say to myself i know they re equal and then some guy comes along and he gives me twice as much in the left and twice as much in the right or he doubles it and i say to myself well i had the same before in the left in the right now. I ve got twice as much in the left and twice as much in the right. I ve still got the same in the left in the right.
I might not know how much i ve got. But i do know that they re equal and of course. I don t put any number there i can say 17 times. The left hand side equals 17 times the right hand side and i m still sweet because i ve got something in my left hand something in my right hand and some guys come along and multiplied everything in my left by 17 and multiplied everything on my right by 17 and in general.
I can say that x. Times. The left hand side where x is any number equals x. To the right hand side.
No matter. What x is x. Can be anything x can be unknown..
It can be this x. I don t know what and i don t know what it is or it could be just a standing symbol community. I can use the same kind of logic to say this if the left hand side equals. The right hand side.
Then the left hand side plus. 16. Let s say equals the right hand side plus 16. Again i m imagining myself.
When i m even when i m doing the most complicated mathematics are doing my research. I still think of myself having something in my left hand something in my right hand. It s some complicated thing like this crud. Here.
Which are just made up out of thin air it might be complicated. I might not understand much about it. But i do know they re equal and then some guy comes along and gives me 16 marbles in my left and 16 marbles in my right hand..
I still know i ve got the same in each hand. I can carry on i can say if the left hand side equals the right hand side. Then i can say something like 1. Over the left hand side equals.
1 over the right hand side again. I ve got something in my left something in my right hand some guy comes along and goes ha. I m gonna take the reciprocal of that left hand side and then he says. I m gonna take the reciprocal of your right hand side too.
And i say well i was confused before and i m confused now because of this reciprocal is business. But i ve still got equality and what we re going to do is to use that trick over and over and over and over again to solve the equations ok. I m going to stop there and ” ..
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