Question Video: Creating Linear Inequalities with One Variable Mathematics

Students in a grade four class were asked the distances in miles, π, which they travel to get to school. All of the students traveled farther than a quarter of a mile, and no one traveled farther than 3 miles. Which of the following inequalities represents the range of distances traveled to school? [A] 0.75 β€ π < 6 [B] 0.5 β€ π < 3 [C] 0.25 < π β€ 3 [D] 0.25 β€ π < 3 [E] 0.75 < π β€ 3

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Video Transcript

Students in a grade four class were asked the distances in miles, π, which they travel to get to school. All of the students traveled farther than a quarter of a mile, and no one traveled farther than three miles. Which of the following inequalities represents the range of distances traveled to school. (A) π is greater than or equal to 0.75 but less than six. (B) π is greater than or equal to 0.5 but less than three. (C) π is greater than 0.25 but less than or equal to three. (D) π is greater than or equal to 0.25 but less than three. And finally, (E) π is greater than 0.75 but less than or equal to three.

So the first thing we want to do in a question like this is remind ourselves about our notation that we use for inequalities. So first of all, we have π₯ is less than π¦. And we know that itβs π₯ is less than π¦ because weβve got the pointy end towards the π₯ and the open side of our inequality sign towards the π¦. And this open side always points towards the greater value. Then we have π₯ is greater than π¦. Then we have π₯ is greater than or equal to π¦. And the difference here is the fact weβve got this line underneath our inequality sign. So this tells us that it can be that value as well. So π₯ is gonna be greater than or equal to π¦. So π₯ could be π¦ or any value greater. And then finally, weβve got π₯ is less than or equal to π¦.

So for our inequality, weβve got our variable π. And then our first bit of information is that all of the students traveled father than a quarter of a mile. So therefore, we know that π is greater than 0.25. And thatβs because 0.25 is the same as a quarter. And we know that itβs just π is greater than not greater than or equal to because it says all of the students traveled father than a quarter of a mile. So they actually traveled more than a quarter of a mile. And then the next bit of useful information we get from question is that no one traveled farther than three miles. So therefore, we can say that π is gonna be less than or equal to three.

You might think, well, why is it less than or equal to? Well, itβs because weβre told that no one traveled farther than three miles, which means that they could have traveled three miles. So therefore, we have to include the βor equals toβ parts of our inequality. So therefore, if we take a look at our possible answers, this is the same as answer (C). So we can say that the correct inequality for our situation is π is greater than 0.25 but less than or equal to three.

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