like people or buildings or materials.

So, let's just start with one. we have x minus 5 is less than 35.

He got 100 percent in all the important things,

Now, as we go to the local picture, we do a lot of local roll outs,

We are full just now.

The key is the trap door, some piece of information, that makes it easy to reverse the encryption.

That's negative 15, which is our solution set.

Every bus is full.

All the buses are full.

I'm satisfied with everything.

Let's say we have an equation y is equal to negative x plus 3.

I would make that a solid dot

And we exclude negative 2 by drawing an open circle at negative 2, but all the values greater than that are valid x's that would solve, that would satisfy this inequality.

Well, think about it.

Check here if you think it's guaranteed to do that.

But then we can shade in everything below 40.

Let's say I have the equation y is equal to x plus 3.

(Laughter) He takes basically everything.

And everything greater than 1 will satisfy this equation.

And then we did a bunch of algebra and we got this equation right here.

So let's say we have the inequality 4x plus 3 is less than negative 1.

And then the cost to you was 200.

We go and tick on run and if everything works well, our test should passed by now.

What are my most expensive resources? What are my most expensive activities?

What you are going to be asking is what are the entire cost to operate a business model.

So they're saying, what are all the x's, that when you subtract 5 from them, it's going to be less than 35?

Everything, everything. One hundred percent. In fact, better.

What this teaches us is that in matching pixels to pixels, we match an entire corresponding line in stereo.

There's a variable cost which is, each widget, they might have used some amount of metal and some amount of energy to produce it and some amount of paint if it's a painted widget.

Every flight to L.A is booked.

You see, the companies they work for keep these human and environmental costs out of sight and off their accounting books.

I also give you something we'll be using in a later quiz and the cost for the step is supposed to be 1.

Everything that satisfies this first equation is on this green line right here, and everything that satisfies this purple equation is on the purple line right there.

In particular, suppose we color all three of the nodes, black.

And they calculated for the top 3,000 corporations, what are the externalities?

And to show this on the number line, we do a circle around 40 to show that we're not including 40.

Let's assume the cost for a bad match, when we match 2 colors that don't correspond, is 20.

He was upset by the low quality and high cost of existing patent reproductions, and so he started to develop a system of dry photocopying, which he patented in the late 1930s and which became the first dry photocopier that was commercially practical in 1960.

So for this final version, let me punish left turns even more

It'll go from 10 3, all the way down to negative infinity.

So let's see if we can find all of the x's that will satisfy this equation.

The moment the lights go down is often the best part, you know?

In fact the locus of all points are the hyperbole in fact is all of the points that satisfy that condition.

It just keeps going on in both directions.

We could just say, oh, you know what?