多步驟方程式 2 (英)

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多步驟方程式 2 (英) : 多步驟方程式 2

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solve for x. we have x-8=x/3 +1/6.
Now the first thing I want to do here
There is multiple ways to do this problem,
What I am gonna do is to simplify the fractions.
I am going to multiply everything times the least common multiple of all
of these guys denominator.
This is essentially,
x over 1, this is 8 over1,
x over 3,
1 over 6
The least common multiple of 1, 3 and 6 is 6.
So if I multiply everything times 6,
it's going to clear out these fractions.
so, these weren't fractions to begin with
So just multiplying them by 6,
so it becomes 6x minus 6 times negative 8 or 6 times 8 is 48
and there is , we are subtracting it right over there,
And then we have x over 3 times 6, let me just write out here
So that's going to be 6 times x over 3, plus,
6 times 1 over 6 .
Or we get, 6x minus 48 is equal to
6 times something divided by 3,
that's the same thing as 6 divided by 3 times that something
that's just going to be equal to 2x plus
6 times one-sixth or 6 divide by 6 is just going to be 1
So that first step cleared out all of the fractions
and now this is just a straight- forward problem
with all integer co-efficients or integers on
either side of the equation.
What we wanna do is, we wanna isolate all of the x
on one side or the other.
we might as well isolate them all on the left hand side
So,lets subtract 2x from both sides,
we want to get rid of this 2x here.
That's why I am subtracting the 2x.
So let's subtract 2x from both sides, and,
on the right hand side, I have 2x plus 1 minus 2x
those cancelled out.
That was the whole point
So , I'm left with just
this 1 over here
On the left hand side, I have 6x minus 2x ,
Well, that's just going to be 4x if I
have 6x of something minus 2 of that something,
I have 4 of that something.
minus 48. And now I can.. lets see I want to get rid of
this 48 on the left hand side, I want only x here.
So let me add 48 to both sides of the equation.
this in a new color! So let me add 48
to both sides of this equation.
And on the left hand side, 4x minus 48 plus 48
those cancelled out, I am left with just a 4x
And on the right hand side, 1 plus 48 is going to be
49. And now I have isolated the x,
but still multiplied by a 4 so to make that
a 1 co-efficent, lets multiply both sides by one-fourth
or you can also that
lets divide both sides by 4.
Anything you do the one side , you have to do to the other
And so you have.. What do we have over here,
4x over 4 is just x,
x is equal to 49 over 4.
That's about as far as we can simplify it
because these don't have any common factors, 49 and 4.
Lets check to see whether 49 by 4 is indeed the answer.
So, let us put it into the original equation
well the original equation is what we have in green here.
before we multiplied it,
before we multiplied by 6.
But in theory we should be able to put it into any of these steps
and x should satisfy it.
Lets do it in our original equation.
So we have x minus 8, so we have
49 over 4 minus 8 should be
equal to 49 over 4 over 3 plus 1 over 6.
So lets see what we can do here, so what we can..
lets see.. we can multiply, well like we did before.
We can multiply both sides of this equation by 6,
that will help simplify a lot of the fractions
here. So if we multiply both sides of this equation
by 6, so we are going to multiply everything
.. everything by 6.
what do we get,
On the left hand side , 6 over 4 is the same thing as 3 over 2
So this is going to be 3 times 49 over 2,
3 times 49 over 2 minus 48
will be equal to
6 divided by 3 is going to be 2, so its
2 times 49 over 4 , which is the same thing as
49 over 2 , and then 6 times one-sixth is plus 1
and lets see , we can, well I am just going to, I am just going to
actually just evaluate them out. I could just essentially have to
you know subtract 49 over 2 from both sides, that will simplify
things, but let me just, let me just figure out what these
evaluate to. So 3 times 49, 49 times 3
you could think about it's going to be 3 less than 50 times 3
so its 147. But less just multiply out 9 times 3 is 27,
4 times 3 is 12, plus 2, is 14. So 147.
This is 147 over 2.
and then lets put this over a denominator of 2.
So 48 is equal to 96 over 2, right
96 divide by 2 is 48. I just multiplied this by 2.
So this is minus 96 over 2, needs to be equal to
49 over 2 plus, and instead of having this 1,
lets write that as 2 over 2.
Now what is 47 minus 96.
So 47 minus a hundred would be,
147 minus a 100 would be 47,
we are going to subtract 4 more than that.
So we are going to have, it's going to be..oh sorry!
We are going to subtract 4 less than a 100
So it's going to be 147 minus 96 is going to be 51,
51 over 2 is equal to 49 plus 2 is 51 over 2.
so it all checks out.

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