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Inequalities word problems

Inequalities are a handy tool for comparing values. For example, if Eric is shorter than Priti who is 158 cm tall, we write E < 158. If Sydney wears skirts when it's warmer than 25 degrees, we say T > 25. If Hayley finishes a race after Lola's 53 seconds, we write H > 53.

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Video transcript

- [Instructor] We're told that Eric is shorter than Priti. Priti is 158 centimeters tall. Write an inequality that compares Eric's height in centimeters, E, to Priti's height. Pause this video and see if you can do that. Alright, so we have Eric's height, which we are using the variable capital E for, And how does it compare? It says Eric is shorter than Priti. So Eric's height is going to be less than whatever Priti's height is, which is 158 centimeters. You could think about it on a number line too. If I were to draw a number line like this, and this is 158 centimeters, Priti's height, Eric's is gonna be less than that 'cause he is shorter. So it would be all of the values that are to the left of, let me do this in another color, that are less than that. Just like that. Let's do another example. Here we are told that Sydney wears skirts when the temperature is warmer than 25 degrees Celsius. Write an inequality that describes T, the temperatures at which Sydney wears skirts. So again, pause this video and see if you can have a go at that. Alright. So when does Sydney wear skirts? When the temperature is warmer than 25 degrees Celsius. Now, warmer means that the temperature is higher than 25 degrees Celsius, or that the temperature is greater than 25 degrees Celsius. And we're using capital T to denote temperature. So we would say capital T, this needs to be higher than 25 degrees, or greater than 25 degrees Celsius. So T is greater than 25. Let's do one last example here. So here we are told that Lola and Hayley are running a race. Lola finishes the race in 53 seconds. Hayley finishes after Lola. Write an inequality that represents H, Hayley's finish time in seconds. Pause the video and see if you can think about this. Alright, so how does Hayley compare to Lola? Hayley finishes after Lola. So what does that mean about Hayley's time? Well, that means that Hayley is going to take more time than Lola to finish the race. So whatever Lola's time is, Hayley's time is going to be longer, or more, or greater than. So Hayley's time is going to be greater than Lola's time, which is 53 seconds, because Hayley finishes after.