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Given information about the lengths of line segments, Sal forms and solves an equation in order to find the lengths of the segments. Created by Sal Khan.
Video transcript
So we have this line segment JL here, and we have point K that also sits on that segment. And they tell us that JK is equal to 7x plus 9. So this distance right over here is equal to 7x plus 9. Then they tell us that JL is equal to 114. So JL is the entire length of the segment. So this entire thing is equal to 114. Then they tells us that KL is equal to 9x plus 9. So this right over here is equal to 9x plus 9. And they say find KL. So they essentially want us to figure out what does 9x plus 9 equal? And to figure that out, we have to figure out what x equals. And lucky for us, they've given us all the information we need. They tell us that the entire segment is 114 long. And they don't give us any units. It's just 114. It has a length of 114. And we know that this segment, JK plus KL, added together, is going to be equal to the length of the entire thing. So we could say that 7x plus 9-- actually let me write it this way. We could write that JK, so the length of segment JK plus the length of segment KL is going to be equal to 114. And we know that the length of segment JFK is 7x plus 9. We know that the length of segment KL is 9x plus 9. And this is going to be equal to 114. And now we just have to break out a little bit of our algebraic skills. So the first thing we might want to do is, let's see, we have two terms that have x's in them. If I have 7 x's, and I were to add that to another 9 x's, that means I'm going to have 16 x's. And then if I have-- so this is just plain old 9, and I add it to another 9. That's going to give me 18. And that's going to be equal to 114. Now I just subtract 18 from both sides. Let me do that explicitly. So I subtract 18 from both sides. On the left-hand side I have 16 x, and on the right-hand side, I'm going to have 114 minus 18. Well, if I were to subtract 14, that would get me to 100. And I'm going to subtract 4 more than that, so that's going to get me to 96. And now we just divide both sides by 16. And let's see, this looks like 96 divided by 16-- we could do it explicitly, but it looks like it's going to be 6. 6 times 10 is 60. 6 times 6 is 36. 60 plus 36 is 96. So we get x is equal to 6. Now we're not done yet. We're not looking just for x. We're looking for the length of KL. KL is 9x plus 9. Let me write that down. So KL is equal to 9x plus 9. They told us that right over there, is equal to 9x plus 9. We just figured out that x is equal to 6. So this is equal to 9 times 6 plus 9. And this is equal to-- 9 times 6 is 54, plus 9, is equal to 63. So KL is equal to 63.