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 17

Accepted Answer

Hello. Today we're gonna be determined the distance between two numbers. So the numbers given to us are five and 28. So let's go ahead and plot that on a number line. So five is going to be the left throws number and 28 is gonna be the right most. What we are asked to determine is what is the absolute distance between these two points. So for five and 28 what we wanted. There's two ways we can find the distance between the two. We can take the difference of 28 or five or we could take the difference of five and 28. Either way it's gonna give us the distance between these two points. So we're going to label them as A. And B. And what we are looking for is the absolute value between A minus B. Or the absolute value of B minus A. So you can choose either or but both of these will result in the same solution. So let's go ahead and choose the left most which is a minus B. We're gonna let A equal to five and we're gonna let B equal to 28. So putting that into the absolute value is going to give us the absolute value of 5 -28. Well 5 -28 is going to result in -23. So what we are left with is the absolute value of -23. Now keep in mind the absolute value only cares about what the absolute distance between the two points is. So negative 23 can also be represented as a distance of 23 between the two points. So all you want to do is just take the positive quantity of negative 23. So the absolute value of negative 23 is just gonna be that is going to be our solution to the problem and the answer to this problem is going to be be So. I hope this video helps you in understanding how to find the absolute distance between two points, and I'll go ahead and see you all in the next video.