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Studying for a test? Prepare with these 5 lessons on Solving equations with one unknown.
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We're told that K is the midpoint of segment, JL. So that tells us that segment JK is going to be congruent to segment KL, that they're going to be the exact same length. And they tell us that segment JK is equal to 8x minus 8. So this distance right over here is equal to 8x minus 8. And then they tell us that segment KL is equal to 7x minus 6, that its length is equal to 7x minus 6. So this length right over here is 7x minus 6. Because K is the midpoint, we know that this length must be equal to this length. So to find JL, we just need to find the whole length. We defined what x is. If we know what x is, then we're going to know what this length is and what this length is. And we could either double one of them or add them together to find the length of the entire segment. So first, let's figure out x. And the best way to figure out x is based on the fact that we know that 8x minus 8 is equal to 7x minus 6. And I just want to reemphasize, how do we know that? Well, they told us that K is the midpoint of JL. This is the midpoint, which tells us that this distance is equal to this distance, or 8x minus 8 is equal to 7x minus 6. Now, to figure out x, we just have to do a little bit of algebra. So let's see what we can do to simplify things. So if we want to get all the x terms on one side-- let's say we're going to get it on the left side-- we could subtract 7x from both sides. So let's do that. Let's subtract 7x from both sides. And if we want to get all of the constant terms on one side, well, let's add 8 to both sides so that we don't have this negative 8 right over here. So let's add 8 to both sides, and let's see what we are left with. On the left-hand side, you don't have an 8 anymore, and 8x minus 7x is just an x. And that's going to be equal to-- on the right-hand side, you don't have any 7x's anymore. And negative 6 plus 8 is just 2. So we get x is equal to 2. But we're not done yet. They didn't say solve for x. They said find JL. So JL is just going to be the sum of JK and KL, or since K is the midpoint, it would just be double JK or double KL. So let's figure out either way. So now we can figure out that JK, the length of segment JK, is equal to 8 times 2 minus 8. We know that x is 2 now. So this is equal to-- well, this is 16 minus 8. This right over here is just equal to 8. And if we wanted to figure out JL, we know that this is halfway, so that this must be 8 as well. And the length of the entire thing, the length of JL must be 16. And if you wanted to spend extra time to make sure that all of the math is consistent, you could put 2 into this right over here. And 7 times 2 is 14 minus 6 is 8. So, once again, you can verify from another direction that this length of segment KL is also 8. 8 plus 8 is 16.