 Okay, so let's talk about inequalities. So I want to look at this function, g of x is x minus 5x. I want to look at that one and just see what my graph looks like. So x squared is what that's supposed to say, minus 5x, because this is x squared here. So I look at my graph and I can see that part of my graph is above the x axis and this stuff right here is going to tell me that y is greater than 0. And then I have y equal to 0 at the x axis. And then anything below is going to be y is less than 0. So I have my graph and it looks like I have, I know it's going to go through 0, 0. Looks something like this. Well, you can see that this x intercept right here and this x intercept right here causes my graph to switch sides of the x axis. Up here, from here over, my graph is above. And from here over, my graph is above. But in between the two, I have the graph is below. So I have three sections and the x intercepts are equal to the boundaries, boundary points. So I really have an interval from negative infinity over here up to this. It looks like 0 and I have between 0 and this one, which is going to be 5. I'll just tell you what that is because we're just looking right now. And then I also have an interval from here over, which is from 5 to infinity. So graphically, when I'm looking at this, if I want g of x to be less than 0, that's going to be my red. My solution for x is less than 0, not equal to, is going to be from 0 to 5. But it can't include either one because my inequality won't allow it. Now, let's look at another one. And we, again, the graph can be very helpful or we could also look at the table. We're going to do both. So negative 3x squared plus x plus 4. And then we want to look at the graph to see what kind of things we have going on here. Okay, well, it's going to be real important that we know what those x intercepts are. But we could use a quadratic formula to help us figure out what those are. Remember, that tells us, gives us the values that we want. So the quadratic 84 is what I want. A is negative 3 coefficient on x squared. B is 1 coefficient on x and C is 4, the constant. And I find out that I have boundary points from at negative 1 and 1 and 1 to 1.3 we can use. So it's going to go from negative infinity up to that negative 1, my boundary point. And this time I can include the negative 1. And then I have between the negative 1 and the 1.3, we'll look at the graph again. And I again can include the 1.3. And then I have from 1.3 over to infinity. Again, let's look at the graph to see that. Negative infinity up to that x intercept, which was negative 1. And then we went to this x intercept, the graph went above it. So it was between 0 or negative 1 and 1.3, my other x intercept. And then from that over to infinity. So if I want to test, I could use a table if I don't want to use the graph. So I test a point somewhere between negative infinity and negative 1. Let's try negative 2. And then I can pick a point between negative 1 and 1.3. So let's try 0. That's always nice. In positive 1.3 to infinity, let's try positive 2. Well, we can plug and chug if we want to. Or we could go to our table. And I'm going to actually let it start at like negative 3. Because I want you to see what happens. So I go to my second graph, look at the table. I'm going to let it tell me what my signs are. So at negative 3, I have a negative 26. At negative 2, I have a negative 10. At negative 1, I have that 0 like I expected. But then when I get on the other side of negative 1, it goes to a positive. So at negative 2, I actually have negative 10. And does that satisfy my inequality? Is it less than or equal to 0? Yes. Then I'm choosing a test point of 0. And it's a positive. And it's a positive all the way looking at this table until I get up to 2. But it's actually at 1.3. So at 0, I actually end up with a positive 4. So it doesn't satisfy. And if I test my point 2, it's at a negative. And if I keep looking through this table forever and ever and ever, now it's going to be a negative. So I know that in that boundary area, it's a negative. And I forget what it was. It was a negative something. But yes, it satisfies. How do I write my answer? I need it to be less than or equal to 0. So that's from negative infinity up to negative 1, including negative 1. Union, because I have another area that is from 1.3, including it to infinity.