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# Equation practice with midpoints

Given an information about the distance of a segment's midpoint from its endpoints, Sal forms and solves an equation in order to find the length of the segment. Created by Sal Khan.

Video transcript

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.