In this lesson, we're going to be translating inequality word problems. When we're translating word problems in math, we're looking for a way to take the information from the word problem and write it over in some type of mathematical way. And in this case, we're working with inequalities. So we're going to do a review of the inequality symbols, and we're also going to talk about what key words we might see in the word problem that will help us to know what inequality is best to use. First, we have greater than and less than. The greater than symbol looks like an arrow that's pointing to the right side. When we're looking at word problems that deal with greater than, some of the words that we might see are greater than, more than, or exceeds. There's many, many more. But this will just give you an idea of what kind of words to keep your eyes looking for. With less than, the symbol that we use is an arrow that's pointing to the left. And the words that we'll see for less than might include less than, fewer than, or below. We could also have symbols that include equal to with them for greater than or equal to. The symbol is the greater than sign with a line underneath it to represent equal to. And words that we might see in the word problems for this symbol include at least, no less than and minimum for less than or equal to this symbol is the less than sign with the line underneath for equal to. And words for this symbol include at, most, no more than, and maximum. And keep in mind, this is just a small list of the key words and phrases that you might come across in word problems. But the important thing is that when you're reading the word problem, to really pay attention to what the word problem is describing. So as you are reading the word problem and trying to figure out what symbol is best to use, you can ask yourself these questions -  Can the value be more than the number? Can the value be less than the number? Can the value be exactly equal to the number? And when you ask yourself these three questions, it should help you to realize what symbol needs to go in your inequality. Let's look at a couple of examples. Kara can spend no more than $15 at the store. Write an inequality that represents the amount of money that Kara can spend. The first thing that we'll need to do when we set up our inequality is to pick what variable we want to use to represent the amount of money that Kara can spend. So since money starts with M, let's use the variable M. Now we want to look back at our word problem to figure out what information they tell us that helps us understand how much money Kara can spend. Well, we see this phrase here no more than $15. So we can ask ourselves, what does that really mean? First, it means that Kara can spend less than $15. She can't go any higher than $15, but she can spend less than it. She can spend $10, $12, anything less than $15. And then we ask ourselves, can she spend exactly $15? And she can. When they say no more than, it means that $15 is the highest she can go, but she can spend exactly $15. So the symbol that we're going to use here is going to be the less than or equal to symbol to show that she can spend exactly $15. So when we put it together, our inequality is M. The money that Kara can spend is less than or equal to 15. Let's look at one more example. Felix needs to score a minimum of 80 points on his exam. Write an inequality that represents the amount of points that Felix must score. First, let's pick a variable to represent the points that Felix must score on his exam. Let's go with the variable P for points. Now we'll look at the board problem to figure out what information they give us to understand how many points he must score. And we see the phrase minimum of 80 points. So now we ask ourselves, does he have to have more than 80 points or less than 80 points? Well, if it says minimum, then that means he really needs to go higher than that. Definitely not less than 80 points. If he scores less than 80 points, then that doesn't meet this requirement. So it is okay for him to score greater than 80 points. And then we ask ourselves, is it okay for him to score exactly equal to 80 points? And in this case, it would be okay. The word minimum means that 80 is the absolute lowest that he can go, but it's still okay if he scores exactly 80 points. So when we put this together in our inequality, we're going to use the greater than or equal to symbol. So we'll have P. The points that Felix must score is greater than or equal to 80. So there we go. Just remember, read the word problem carefully, pick your variable, and then ask yourself those questions to figure out what inequality symbol is best to use to put it all together.