Mode 1 returns the one tailed test, Mode 2 returns the two tailed test.

For the velocity of the two trains.

And so you have this 15 trillions divided by 1.025 or you can divide both sides by 1.025 and multiply both sides by the real GDP.

If the x minus 1 is less than 0, if we add 1 to both sides of that equation that tells us so x minus 1 is less than 0.

Now, if this was an equality, your natural impulse is to say, hey, let's divide both sides by the coefficient on the x term, and that is a completely legitimate thing to do divide both sides by negative 0.5.

So these are our two situations when we're multiplying both sides.

The amount and level of wages becomes a question of negotiation.

Let's multiply both sides of this equation by mu, and mu of x is just x.

336 plus x is equal to 440.

And now we could square both sides of this equation right here.

So let's just do the same step.

You have nine x is equal to eleven.

And now I want to get rid of this negative 5.

Just so that we feel a little bit more comfortable with all of our Ys sitting on the 1 side.

Let's say that x is equal to t minus c.

I can say this is going to be x plus something squared.

So we get x minus a squared is equal to I'm moving both of these terms to the right hand side.

So you could say 8 x over 13 is equal to 4 fifth times x minus fifteen.

Let's say that v and I'll do v in a different color let's say that v is equal to y over x.

Let me scroll this down a little bit.

We'll do it onto the left hand side.

There were branches on both sides.

So I need to take half of this and then square it and then add it to both sides.

I'm going to multiply everything by negative 1.

And so we want to figure out what r is.

That does simplify a little bit.

You get 2x is equal to negative 5.

You get 2x is equal to positive 5.

I'm just trying to help myself remember this thing.

We have to separate the y's from the x's.

Anyway, I think you get that.

So going back to how we did these problems before.

I'm going to make this p pink.

Well, I'd... talk to him.

It should maybe start becoming a little bit clearer what the solution here is, but let's just keep going forward.

This is 146 is equal to 180.

And then we can solve each of these.

You could get one solution is negative 5 2.

So you get equals x squared over a squared plus 1.

And this is the other one that you just take a straw, and you just put a stick inside and you make two half cuts.

So I want to get rid of this negative 5, and I can do that by adding 5 to both sides of this equation.

Well, we've been doing things like if I said that y is equal to, I don't know, 3x.

Or a one y on the right hand side, I can divide both sides by 13.

But all these have the same mass. That's why I wrote Y on all of them.

Minus that pink p times 1 plus i.