We're told the K is themidpoint of segment, JL. So that tells usthat segment JK is walking to it is in congruentto segment KL, that they're going to bethe exact same length. And they tell united state that segmentJK is same to 8x minus 8. So this distance ideal overhere is same to 8x minus 8. And then they tellus that segment KL is same to 7x minus 6, the itslength is same to 7x minus 6. So this length rightover here is 7x minus 6. Since K is themidpoint, we know that this size mustbe same to this length. So to find JL, we just needto uncover the entirety length. We defined what x is. If we know what xis, climate we're walk to recognize what this lengthis and what this size is. And also we might eitherdouble among them or add them together to find thelength the the whole segment. So first, let's figure out x. And also the best way to figureout x is based upon the fact that we understand that 8x minus8 is same to 7x minus 6. And also I simply want come reemphasize,how perform we know that? Well, they told us thatK is the midpoint that JL. This is the midpoint,which tells united state that this street is equal tothis distance, or 8x minus 8 is equal to 7x minus 6. Now, to figure outx, us just need to do a tiny bit of algebra. Therefore let's see what us cando to simplify things. Therefore if we want to get allthe x state on one side-- let's speak we're going come getit on the left side-- we could subtract 7x from both sides. For this reason let's carry out that. Let's subtract 7xfrom both sides. And if we desire to acquire all ofthe continuous terms ~ above one side, well, let's add 8to both political parties so that we don't have actually thisnegative 8 appropriate over here. So let's add 8 toboth sides, and also let's watch what we space left with. Top top the left-hand side, youdon't have actually an 8 anymore, and 8x minus 7x is simply an x. And that's walking to be equalto-- ~ above the right-hand side, girlfriend don't have any 7x's anymore. And an adverse 6 to add 8 is just 2. Therefore we obtain x is same to 2. However we're no done yet. Castle didn't say solve for x. They said uncover JL. Therefore JL is simply going tobe the amount of JK and KL, or because K is the midpoint,it would simply be twin JK or double KL. So let's figure out one of two people way. So now we can figure out thatJK, the length of segment JK, is same to 8 time 2 minus 8. We understand that x is 2 now. For this reason this is same to--well, this is 16 minus 8. This right over hereis just equal to 8. And if us wantedto figure out JL, we understand that this is halfway,so the this must be 8 as well. And also the length of the entirething, the length of JL must be 16. And also if you wanted to spendextra time to make sure that all of themath is consistent, you could put 2 intothis appropriate over here. And 7 times 2 is14 minus 6 is 8.
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So, once again, you canverify from another direction the this length ofsegment KL is additionally 8. 8 plus 8 is 16.