We can divide both sides of this inequality by 3.

Precedence and Associativity,

So we're going to have our precedence and associativity.

Afterwards, we have about a dozen or so binary rules.

Divide

Division

I've written a grammar on the left.

Plot them out on complex plane, and see what happens when you multiply them, when you divide them, when you add them, when you subtract them.

Multiply

Multiplication

Now, to isolate the y, you can either multiply both sides by negative 1 12 or you could say let's just divide both sides by negative 12.

ERROR DIV BY 0

Integer division

And we learned, up here, in this part of the video,

In this video, I want to tackle some inequalities that involve multiplying and dividing by positive and negative numbers, and you'll see that it's a little bit more tricky than just the adding and subtracting numbers that we saw in the last video.

So dividing by 1 2 is the exact same thing as multiplying by 2 1.

Well, the smallest number that is divisible by 4 and 8 is 8.

What this tells us is that we do parenthesis first and expeonentiation takes priority over everything else here, so we have to evaluate these exponents before we multiply anything or before we subtract anything.

So this thing right here is the same thing as 3 5 times so this is our 3 5 right here, and instead of a division sign, you want a multiplication sign, and instead of a 1 2, you want to take the reciprocal of 1 2, which would be 2 1 so times 2 1.

Now if we multiply both sides by x plus 2, x plus 2 is a negative number.

That minus two is here and this fourx is here.

Multiply, expressing the product in scientific notation.

We just substituted that for that to get this right here.

This means it takes less time to do our recursive walk and interpret it, and we have fewer multiplications.

Never have to worry about that.

That's called dimension analysis.

Well, we have a little bit of experience doing this.

Now, we can just multiply both sides of this equation by minus thirteen over three.

And then our denonminator, two numbers.

The important thing you need to realize, though, when you do it with an inequality is that when you multiply or divide both sides of the equation by a negative number, you swap the inequality. you swap the inequality

Those are all binary operators.

And this is, you know, another scalar multiplication.

P is for Parenthesis, E is for Exponents, M and D are for multiplication and division and they are really at the same level of priority and then addition and subtraction are at the same level.

These are just multiple ways of stating the same thing.

Let me switch colors.

But just understand that this is the same thing as this.

OK.

So we got a lot of twos

So this is just our integration by parts formula.

Your top priority's going to be your parentheses, after that you're going to have your exponents, after that you have multiplying and dividing, and after that you have addition and subtraction.

Now, we take that 4x squared and we multiply it by our expression.

If volume goes down, pressure goes up, and that makes sense.

They have to be positive.

Blah, blah, blah, blah, blah the part here at the bottom is the most important

The CPU could do the four fundamental functions of arithmetic so addition, multiplication, subtraction, division which already is a bit of a feat in metal, but it could also do something that a computer does and a calculator doesn't this machine could look at its own internal memory and make a decision.