 This video will talk about inequalities and word problems. Our first example says Liz has scores of 90, 85, 83, 92 on her first four algebra tests. What score does she need to get on her fifth test so that she has at least a 90% average? Well, what we need to know, what our unknown is here is X is going to be equal to the score on the fifth test. But the one thing you have to remember is that whatever you have on one side has to be the other. And on this side of the at least, we have the word average. We want a 90 average. So we need the average of the five has got to be at least 90 average. Well, how do you average? You take all your values, so we've got 90 plus 85 plus 83 plus 92 plus the fifth one because we're averaging five of them and you divide by the number of things you're working with and we have five. And then we have 90 on this side, but what goes with at least? Think about it. It means at least 90. So I want 90. So I want it to be equal to 90, but I want it to be bigger than 92. So this average has to be greater than or equal to 90. If I take 90 plus 85 plus 83 plus 92, that ends up being 350 plus X over five has to be greater than or equal to 90 and I've got a fraction in my problem. So I'm going to multiply both sides by that denominator. And on the left side, nice things happen because I have a numerator and denominator that are five and I'm just left with 350 plus X on the left-hand side and that's going to be greater than or equal to five times 90, which is going to be 450. And now we just solve the equation. So minus 350 on both sides and that will tell us that X has to be greater than or equal to 100 when we subtract. So she needs to get a perfect score and if there's extra credit, she needs a perfect score plus extra credit to get at least a 90 average. The cost of rent a car for a week from BMW rentals is 304 plus 30 cents per mile. How many miles can be driven if you have at most $960 to spend on a rental car? So we know that the cost has to be at most $960. Well, what is the cost? Well, cost is made up of the $304 plus the 30 cents per mile. So we have 304 plus .30, which is the 30 cents per mile means times the number of miles. And we're going to let M equal the number of miles driven. So now we need to, we've got the cost and so we have here. And then if we do at most, that means at most means it could be $960, but it can't be any more than that. So this cost has to be less than or equal to that $960. So now we have an inequality that we're ready to solve. So to solve it, we're going to say we're going to subtract our 304 from both sides and I've got my nice little calculator over here so I can let it do all my calculations quicker. So $960 minus 304 is going to be equal to 656. So I now have .30M, which is less than or equal to that 656. And then I just have to divide by the .30 to get to M by itself. So .30 divide there and divide by .30 on this side and this side I get M. And then it's going to be less than or equal to and come over here and we will divide our 656 by .30. And we find out that that is 2186.66 repeating or 667. So when I write my sentence, I'll just round that to the nearest 10th maybe because that's probably the way that they do it in real life. So I would say that you can drive and it says less than or equal to this many miles. So at most 2186.7 miles.