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### Course: Algebra basics > Unit 8

Lesson 1: Equations & geometry- Equation practice with segment addition
- Equation practice with segment addition
- Equation practice with midpoints
- Equation practice with midpoints
- Equation practice with vertical angles
- Equation practice with vertical angles
- Equation practice with complementary angles
- Equation practice with supplementary angles
- Equation practice with angle addition

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# Equation practice with segment addition

If we split a line segment into two segments, the length of the total segment equals the sums of the lengths of the two smaller segments. We can make an equation out of the given information. After we solve for the value of x, we can substitute that value back into the expression for the length we are seeking. Created by Sal Khan.

## Want to join the conversation?

- the captions said jfk lmao(19 votes)
- Khan academy saved me(11 votes)
- I agree with that.(7 votes)

- Is there anyone on Khan Academy anymore? All these comments are from years ago. I see no active or recent questions. If I ask a question will it even get answered?(3 votes)
- There are plenty of people on Khan Academy. Sometimes users ask questions more often than other times.(3 votes)

- I like o know if monkes eat more than bannanas(4 votes)
- Wait, if I have a perpendicular set of lines and I needed to use this method to figure it out, how would I do that? I don't even know what it's called because I was late to starting school and I need help DX(4 votes)
- If you have two lines that are perpendicular, it means that they intersect each other at a 90-degree angle. One way to determine if two lines are perpendicular is by checking the slopes of the lines.

If the slopes of two lines are negative reciprocals of each other, then they are perpendicular. The negative reciprocal of a slope is found by flipping the fraction upside down and changing its sign. For example, the negative reciprocal of 2/3 is -3/2.

To use this method to determine if two lines are perpendicular, you need to find the slopes of the two lines, and then check if they are negative reciprocals of each other. If they are, then the lines are perpendicular.

For example, if you have two lines with slopes of 2 and -1/2, you can determine if they are perpendicular by finding the negative reciprocal of each slope.

The negative reciprocal of 2 is -1/2

The negative reciprocal of -1/2 is 2

Since the slopes of the two lines are negative reciprocals of each other, the lines are perpendicular.(1 vote)

- where does the subtracting 18 come from?(2 votes)
- To get x on one side of the equation so Sam subtracted 18 from each side because what you do to one side, you have to do to the other(2 votes)

- If JK+KL=114 (1:28) does that mean KL+JK also equals 114?(2 votes)
- Yes, because it doesn't matter which order things are added together in. (commutatative property of addition)(2 votes)

- this is a little confusing sometimes and I need help(2 votes)
- what do you need help with(1 vote)

- Why is y used as secondary (as in x + y = 2x)(2 votes)
- So how do you know which one to use at the right time? (like subtraction,addition,division, and multiplication.)(2 votes)

## 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.