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代數: 線性方程式 3 (英) : 多個變數與常數的線性方程式
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- Welcome to my presentation on level 3 linear equations
- So lets make up a problem. Let's say I had
- x+2x+3=-7x-5.
- Well, in all these linear equations, the first
- thing we try to do is get all of our
- variables on one side of the equation and
- then get all of our constant terms and then
- it will become a level one linear equation.
- So the first thing we can do is
- we can simplify each of the sides.
- Well, on the left side we have this x+2x.
- Well, what is x+2x?
- Well that's like saying I have one apple
- and now I have two apples so here I have
- one x and now I have two more x's
- that I'm adding together so that equals 3x.
- 3x+3=-7x-5.
- Now let's bring the 7x over onto the left hand side
- and you can do that by adding 7x to both sides.
- This is a review.
- We're adding the opposite so it's negative 7x
- so we add 7x so that's why.
- And we do that because on the right side
- these two will cancel and the left side
- we get 10x+3= and on the right side
- all we have left is the -5.
- Almost there. Now we're at a level 2 problem.
- Now we just have to take the three and move it
- to the other side and we can do that by
- subtracting three from both sides.
- The left hand side; the threes cancel out.
- That why we put them there in the first place.
- And you have 10x= and then -5 minus 3
- well, that equals -8.
- Now, we just multiply both sides of this equation by
- 1/10, or the reciprocal of 10 which is the
- coeffecient on x.
- You could also...
- Some people will say we are dividing both sides
- by 10, which is essentially what we are doing.
- If you divide by 10, that's the same thing as
- multiplying by 1/10.
- Well anyway on the left side, 1/10 times ten
- well, that equals one so we're just left with x equals
- -8/10. That can be reduced further.
- They both share the common factor, 2.
- So you divide by 2. That's a minus 4 over 5.
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