And I'd try out any x that's less than or equal to 3 and verify for yourself that it does indeed satisfy this inequality.

It just keeps going on in both directions.

And everything greater than 1 will satisfy this equation.

Any x that is less than or equal to 3 will satisfy this equation.

You get x could also be equal to positive 5 2.

When x is 0 here, 0 plus 3 is equal to 3.

So the end result is that this is equivalent to just returning 0, which satisfies the problem constraints.

And clearly, they positive 3 and negative 6 their product is negative 18.

All of these things that I'm shading in green would satisfy the inequality.

So something that meets both of these constraints will satisfy the equation.

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.

Nothing satisfies both of these, but there are things that satisfy both of these.

And if you just think about it reasonably, all of these equations are about finding an x that satisfies this.

So that equals 0.

Two should work for that.

We serve at your whim.

So two is greater than one.

Are you getting all this? !

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

But not anything that satisfies this one is going to satisfy that one.

And then we could use multiple arguments. The vertical angle argument, the supplementary argument two ways, or the corresponding angle argument to say that, hey, this must be 70 degrees as well.

If Hands Up turns out well,

So even with our hand drawn graph, we were able to inspect it and see that, yes, we were able to come up with the point 3 comma 3, and that does satisfy both of these equations.

But we say, look, both of these things have to be true.

So this is price, and this right over here is quantity.

So we have 1 2x7 13 ?I put a ? because we don't know if it satisfies.

Adam and Oz both saved an hour of time.

So that point represents Abby's and Ben's earnings that satisfy both constraints.

Now, let's verify that if we substitute y1 and its derivatives back into this differential equation, that it holds true.

I will take them in. Happy now?

Well, I mean we know if you say something has to be less than minus 2 and less than 1, just saying that it's less than minus 2 will do the job.

He has eight valence electrons.

That's less than 35.

Sports is to war as pornography is to sex.

And x has to be less than minus 4.

Are you satisfied or dissatisfied?

Now, what if I were to ask you, is there an x and y pair that satisfies both of these equations?

Because if it's greater than 1 it's definitely going to satisfy this constraint over here.

They seem a little past their peak, but even so we enjoyed the beautiful cherry blossoms.

Let me show you an example. Here's a balanced binary tree with 20 nodes.

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

And there are x's that satisfy these two constraints.

There weren't x's that satisfy these two constraints.

They will feed your people.

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