From Equations to Inequalities 05:18 minutes

Video Transcript

Transcript From Equations to Inequalities

Looks like fishing season has begun! Meet Wade. He's interested in protecting the fish population from overfishing, so they remain in our oceans forever. However, Wade's brother, Skeeter, earns a living from fishing, so he wants to catch as many as possible and hasn't bothered to learn the regulations. In order for Wade to help his brother understand the laws, he'll have to go from Equations to Inequalities. The fishing regulations state that each fisherman is allowed to catch exactly 999 lbs. of fish per month. So, let’s look at how many fish he caught in each of the last 3 months. Let's use the variable 'f' to represent the amount of fish Skeeter catches in pounds. In the first month, Skeeter caught 999 lbs. of fish. What symbol can we use to relate the amount of fish he caught with the legal limit? Out of all the signs and symbols available to us, we should use the equal sign. The numbers on either side of an equal sign have the same value. During the second month of his fishing trip, Skeeter caught 800 lbs. of fish. What symbol can we use to relate the numbers 800 and 999? We know that 800 is not the same as 999. This is no longer an equality, but an INequality. So we have to use a different symbol to relate these numbers. The symbol we use is called the less than symbol, since the smaller of the two numbers comes first. This is read as: 800 is less than 999. In Skeeter's third month of fishing, he caught a BIT more than 999 lbs. of fish...1250 lbs., to be exact. So, how do we relate how much fish Skeeter caught in month 3 with the fishing regulations of 999 lbs. of fish per month? If the number on the left is larger than the one on the right, we can relate the two numbers by using the greater than symbol. This symbol is similar to the less than symbol, but points in the opposite direction. Poor Skeeter, since he overfished in the 3rd month, he's gotta pay a fine! Now that we know the greater than and less than symbols, let's see if we can express, in math, the situations where Skeeter -- and the other fishermen -- will and won't have to pay a fine. Since catching under 999 lbs. of fish is okay, and there's nothing wrong with catching exactly 999 lbs. of fish, is there another sign we could use? In fact, there is! We can make a small addition to the greater than symbol, and it makes all the difference. If we combine the less than sign with an equal sign, we get something that looks like this. Now we have a mathematical sentence that correctly describes situations where fisherman will not have to pay a fine. Speaking of regulations, since catching 1,000 lbs. of fish or more is totally NOT okay, is there another sign we could use? You betcha! If we combine the greater than sign with an equal sign, we get something that looks like this. Now, we have mathematical sentences that correctly describe the fishing regulations. To describe each situation, we used different signs. The sign for equality is the equal sign. Use this sign if the two values are exactly the same, like 'x' is equal to 'y', or 999 is equal to 999. For an inequality, however, there are four different signs at our disposal. We use the 'less than' sign when the value on the left side of the inequality is smaller than the value on the right, like 800 is less than 999. We use the 'less than or equal to' sign if the value on the left side of the inequality is smaller or is the same as the value on the right side. 800 and 999 are both less than or equal to 999. We should use the 'greater than' sign when the value on the left side of the inequality is larger than the value on the right, like 1,250 is greater than 999. Finally, we use the 'greater than or equal to' sign if the value on the left side of the inequality is larger than the value on the right side, or is the same. Since 1,250 is at least equal to 1,000, we can use the greater than or equal to sign. Let's get back to Skeeter and see how many pounds of fish he caught today. Huh?! Have you ever seen that species of fish before?