Solve for y and check your solution.
20 minus 7y is equal to 6y minus 6.
So what I really want to just do is
isolate all of the y's on one side of this equation.
And then if there's some coefficient in front of it,
I can divide both sides by that coefficient.
And I could isolate the y on either the left side
or the right side of the equation.
Actually, let me do it both ways.
So first, it looks like it'll be a little bit simpler if I
isolate it on the right hand side,
and I'll show you that in a second.
So if I want to put all of the Y's on the right hand side,
how could I get rid of the Y's on the left hand side?
I have a minus 7y, or you could use the negative 7y.
I can add 7y to both sides of this equation.
So I'm just adding 7y to both sides.
Then the left hand side of the equation--
we have 20 minus 7y plus 7y.
Those are going to cancel out.
You're going to be just left with 20.
And on the right hand side of the equation,
you're going to have 6y plus 7y, which is 13y.
And then you have your minus 6.
And I want only y's, or multiples
of y's, on the right hand side of the equation.
So I need to get rid of this minus 6 over here.
So let's add 6 to both sides of this equation.
And then on the right hand side, I have 13y minus 6 plus 6.
That's just 13y-- got rid of the minus 6.
And I have 20 plus 6.
So that is 26.
So I get 26 is equal to 13y.
I've isolated the y on the right hand side,
although it's being multiplied by 13.
So if I just want a y on the right hand side
or 1y on the right hand side, I can divide both sides by 13.
Or the equivalent statement would
be to multiply both sides by 1 over 13-- same thing.
So let's divide both sides of this equation by 13.
On the right hand side, 13 times y divided by 13.
Well, that's just going to be y.
So this is just y.
And then 26 divided by 13-- that is 2.
So our solution we got is y is equal to 2.
Now I want to take a step back.
Why did I say it would be a little bit easier
to put the y's on the right hand side of the equation?
Well, because that's the way I got a positive coefficient
in terms of y.
I got 13y.
If I had subtracted 6y from both sides,
I would have got a negative 13 on the left hand side, which
would have been a legitimate thing to do.
Let me just show you what I'm talking about.
So I could have done the problem this way-- 20 minus
7y is equal to 6y minus 6.
Now let me just subtract 6y from both sides.
So minus 6y, or negative 6y, from both sides.
The left hand side over here is 20 minus 13y.
The right hand side-- I got rid of that 6y.
I just have the minus 6 here, or it's just a negative 6 now.
And now I can subtract 20 from both sides
to isolate the y's on the left hand side.
So I'm subtracting 20 from both sides.
I'm doing that to get rid of this 20.
And so on the left hand side, I have a negative 13y,
and on the right hand side, I have a negative 26.
Now I want to divide both sides of this equation
by negative 13, and what do I get?
Negative 13 times something divided by negative 13
is just that something.
I just get a y.
And then negative 26 divided by negative 13 is 2.
So I did it two different ways.
Over here, I isolated the y's on the left hand side.
Over here, I did it on the right hand side.
I picked the right hand side first
so that everything stays positive,
but this is an equally valid way to do it.
Now the last thing I want to do is just make sure
that we got the right answer.
We should probably feel pretty comfortable.
We got the same answer doing it two different ways,
but let's actually check it.
Let's put y equal 2 back into the equation
and verify that we get the equality.
So we have 20 minus 7y is 2.
So 7 times 2 should be equal to 6 times 2 minus 6.
So this should be 20 minus 14.
I want to do multiplication first-- order of operations.
So this is 20 minus 14 should be equal to 6 times
2 is 12 minus 6.
20 minus 14 is 6.
12 minus 6 is 6.
6 is, indeed, equal to 6, so it all checks out.