In Exercises 67–74, express the distance between the given number...

Question

In Exercises 67–74, express the distance between the given numbers using absolute value. Then find the distance by evaluating the absolute value expression. −2 and 5

Accepted Answer

Hello. Today we're going to be determined the distance between two integers. So the industry is given to us is 17 and nine. So let's just go ahead and plot these two integers on a number line. So -17 is going to be the left most and positive nine is going to be the right most. Now when the when the problem states to determine the distance between them, what we are asking for is what is the absolute distance between these two numbers. And the way that's gonna work is if we label 17 as A. And nine as B. If we take the absolute value of B minus A, that's going to give us this entire distance and vice versa. If we take the difference of A and B and take the absolute value of that distance is going to give us the entire distance from negative 17 to 9. So we have two options here, we can use the absolute value of A minus B. Or we can use the absolute value of B minus A. Let's go ahead and pick this side either or will work. So we're gonna let a equal to negative 17 and we're gonna let B equal to nine. So putting this into the absolute value is gonna give us the absolute value of -17 -9. Now -17 -9 is going to result in -26. So what we have now is the absolute value of -26. So keep in mind the absolute value means that we only care about the absolute distance between the two numbers so far. we are told that's negative 26 but that means that the distance between the two numbers is going to be 26. So what the absolute value does is a light to just take the positive value of the given number here, and the solution to this problem is going to be and the answer to the problem is going to be D. So I hope this video helps you in understanding how to find the absolute distance between two numbers, and I'll go ahead and see you all in the next video.