Did I just say equation?

I shouldn't call it an equation.

So it's negative 2.13.

The left hand side just becomes an x.

That's negative 3x.

So I can add 5 to both sides of this equation.

In this video I want to do a couple of inequality problems that are deceptively tricky.

And everything larger than that is a valid y, is a y that will satisfy the inequality.

That won't change the inequality.

That's the equation of this line.

But remember, when you multiply or divide both sides of an inequality by a negative number, you swap the inequality.

But we have to remember, when you multiply or divide both sides of an inequality by a negative number, you have to swap the inequality.

We have x minus 1 over x plus 2.

That won't change by adding or subtracting the same thing to both sides of the inequality.

Is two comma five a solution of this system?

So two is greater than one.

You do an inequality or I guess you could call this an inequality equation you do it exactly the same way you would do a normal linear equation.

There's really not much new here.

And you could try out any value less than 1 10 and verify that it will satisfy this inequality.

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

We're multiplying both sides by a positive.

That just ends up with a zero.

Numbers.

There's language gaps, there's ethnicity and racial gaps, there's age gaps, there's gender gaps, there's sexuality gaps, there's wealth and money gaps, there's education gaps, there's also religious gaps.

Or a more natural way to write it since we actually have a bunch of greater than signs, that this is actually the

Gaps

So if we divide both sides of this by negative 3, we have to swap this inequality.

These 5's cancel out.

Greater than or equal to negative 15 is the solution.

So, for those of you that are familiar with probability, this equation might make sense, if you're a little less familiar with probability, you know, here's how I read this expression, this is the probability that y is equals to one, given x instead of given that my patient has, you know, features X.

But the important point here 1) hopefully, you realize the difference between an expression and an equation.

6 would satisfy it, 10 would satisfy it, 100 would satisfy it.

But we can operate on all of them at the same time, this entire inequality.

0.942.

So 4j minus 100 I just added all the constant terms has to be less than or equal to 500.

So this is really all you have to remember

But in the ones we've solved so far, you solved for a particular x.

I take 15 away from this and from that, the greater than or equal sign will still apply.

This is just an expression.

Gap

So if I multiplied this entire inequality by 0.942 I get, on this left hand side over here I have negative 2.262 times 0.942 and it's a positive number that we're multiplying the whole inequality by, so the inequality signs are still going to be in the same direction is less than we're multiplying this whole expression by the same expression in the denominator so it'll cancel out.

So now that we divided both sides by a negative number, by negative 3, we swapped the inequality from greater than to less than.

It's actually important to realize the distinction between an expression and an equation.

Whatever we do to one side of the equation we have to do it on the other side

Well this is the exact same equation.