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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代數: 線性方程式 3 (英)

代數: 線性方程式 3 (英) : 多個變數與常數的線性方程式