Inequality Problem Solving

And the easiest one I can think of is multiply both sides by 3.That'll get rid of the 3's in the denominator. And then 3 times negative 25 over 3 is just negative 25.They're easy to think about-- oh, it's a little bit more than 8. So 8 and 1/3 is equal to-- the denominator's going to be 3. So this thing over here is the same thing as 25 over 3. So it's 2/3 is greater than negative 4y minus 25 over 3.

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I just swapped the order, you could say negative 9/4 is less than y.

Or if you want to visualize that a little bit better, 9/4 is 2 and 1/4, so we could also say y is greater than negative 2 and 1/4 if we want to put it as a mixed number.

So let's multiply both sides of this equation by 3. And then I'm going to multiply the right-hand side. Well, one point that I want to point out is that I did not have to swap the inequality sign, because I multiplied both sides by a positive number. Now, we want to get all of our constant terms on one side of the inequality and all of our variable terms-- the only variable here is y on the other side-- the y is already sitting here, so let's just get this 25 on the other side of the inequality.

If the 3 was a negative number, if I multiplied both sides by negative 3, or negative 1, or negative whatever, I would have had to swap the inequality sign. So the left-hand side, we have 3 times 2/3, which is just 2. And we can do that by adding 25 to both sides of this equation.

We have the inequality 2/3 is greater than negative 4y minus 8 and 1/3.

Now, the first thing I want to do here, just because mixed numbers bother me-- they're actually hard to deal with mathematically.

So let's add 25 to both sides of this equation.

And with the left-hand side, 2 plus 25 five is 27 and we're going to get 27 is greater than.

I encourage you to watch it, it is actually fascinating. Write an inequality to represent, s, the speeds at which a moving object creates a sonic boom.

So we'll start an inequality, we'll do what they told us to. S has to be, they say when an object travels faster than the speed of sound.

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