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so we have this line segment Jael here and we have point K that also sits on that segment and they tell us that J K 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 and then tell us that KL is equal to 9 X plus 9 so this right over here is equal to 9 X plus 9 and they say find KL so they essentially want us to figure out what does 9 X 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 has length 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 we could say that 7x plus 9 actually let me write it this way we could write we could write that JK so the length of segment JK plus the length of segment KL plus KL is going to be equal to 114 114 and we know that the length of segment JK is 7x plus 9 7x plus 9 we know that the length of segment KL is 9x plus 9 so plus 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 we have two terms that have X's in them if I have seven if I have seven X's and I were to add that to another nine X's that means I'm going to have 16 X's 16 X and then if I have so this is just plain old 9 and I add it to another nine that's going to give me 18 and that's going to be equal - 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 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 sick 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 don't we're not looking just for X we're looking for the length of KL KL is 9 X plus 9 let me write that down so KL is equal to 9 X plus 9 they told us that right over there is equal to 9 X 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