Example 2: Variables on both sides | Linear equations | Algebra I | Khan Academy

Solving Equations 2

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[tmic]

This guy is better than all my math teachers

[gaminghats]

3:10      . did he just put algebra and fun in the same sentence?

[joelyajure]

YouTube math videos are better than teachers

[impanagops]

This is so helpful! I have been struggling with this topic for a week but now I understand!

[분꽃나무]

23강
Algebra 1 - Unit 2 - L1 - 3/5
3/5 Equations with variables on both sides: 20-7x=6x-6
(= Example 2: variables on both sides)

1. 0:01
2. 0:10
And we need to solve for x.
3. 0:12 0:13 we 0:14 which 0:16 on 0:17 0:18
So the way I like to do these is we just like to separate the constant terms, which are the 20 and the negative 6 on one side of the equation.
(ㅈㄷㅂㅇ) 그래서 제가 좋아하는 방식은 방정식의 한쪽에 20과 -6인 상수항을 분리하는 것입니다.
constant term 상수항
4. 0:19
I'll put them on the right-hand side.
상수항을 우변에 놓겠습니다.
5. 0:20 we'll 0:21 0:23 we'll 0:24
And then we'll put all the x terms, the negative 7x and the 6x, we'll put it all on the left-hand side.
그런 다음 모든 x항, 즉 -7x와 6x를 모두 좌변에 놓을 겁니다.

6. 0:26 0:27 let's 0:28
So to get the 20 out of the way from the left-hand side, let's subtract it.
7. 0:30
Let's subtract it from the left-hand side.
8. 0:32 anything 0:33 you 0:34
But this is an equation, anything you do to the left-hand side, you also (have) to do to the right-hand side.
9. 0:36 in 0:37 anything 0:39 to the 0:40 0:41
If that is equal to that, in order for them to still be equal, anything I do to the left-hand side (I) have to do to the right-hand side.
10. 0:42 let 0:44
So I subtracted 20 from the left, let me also subtract 20 from the right.

11. 0:48 0:50
And so the left-hand side of the equation, 20 minus 20 is just 0.
12. 0:51 0:52 / 0:53
That was the whole point, they cancel out. Don't have to write it down.
그게 요점이고 그것들은 상쇄됩니다.
13. 0:54 0:55 0:56
And then I have a negative 7x, (it) just gets carried down.
(ㅈㄷㅂㅇ) 그리고 -7x가 나오면 그냥 넘어갑니다.
ㆍㆍㆍ
carry down 1. 가지고 내리다 2. 후세에 전해지다 3. 이월하다

14. 1:01
And then that is equal to the right-hand side of the equation.
15. 1:05 / 1:07
I have a 6x. I'm not adding or subtracting anything to that.
16. 1:09
But then I have a negative 6 minus 20.
ㆍㆍㆍ
but then 하기는, 하지만 또
but then (again) 2. 그도 그럴 것이 1. 아니 정반대로

17. 1:13 and 1:16 below that 1:17
So if I'm, if I'm already 6 below 0 on the number line, and I go another 20 below that, that's at negative 26.
(ㅈㄷㅂㅇ) 따라서 수직선에서 이미 0 아래 6에 있고 그 아래로 20을 더 내려가면 -26이 됩니다.
(ㄱㅅ) -6과 -20의 합과 같으므로 계산하면 -26이 됩니다.
number line 수직선

18. 1:21 1:22
Now the next thing we want to do is we want to get all the x terms on the left-hand side.
19. 1:25 so 1:27
So we don't want this 6x here, so maybe we subtract 6x from both sides.
20. 1:30 and 1:35 / 1:37
So let's subtract 6x from the right, subtract 6x from the left, and what do we get? What do we get?

21. 1:39
22. 1:46 1:49
23. 1:52
24. 1:56
That was the whole point by subtracting negative 6x.
25. 2:00 2:02 depending 2:03 2:05
And then we have just a negative 26, or minus 26, depending (on) how you want to view it, so negative 13x is equal to negative 26.

26. 2:10
Now, our whole goal, just to remember, is to isolate the x.
이제 기억해야 할 우리의 전체 목표는 x를 분리하는 것입니다.
27. 2:14
We have a negative 13 times the x here.
여기에 x의 마이너스 13배가 있습니다.
28. 2:16 if we divide 2:19
So the best way to/ isolate it is if we have / something times x, if we divide by that something, we'll isolate the x.
따라서 이를 분리하는 가장 좋은 방법은 x를 곱한 값이 있는 경우 이를 그 값으로 나누어 x를 분리하는 것입니다.
29. 2:22 2:23
So let's divide by negative 13.
30. 2:27
Now, you know by now, anything you do to the left-hand side of an equation, you have to do to the right-hand side.
지금쯤이면 방정식의 좌변에서 하는 일은 우변에서도 해야 한다는 것을 아실 겁니다.
ㆍㆍㆍ
by now 지금쯤은, 지금은 벌써.

31. 2:33
So we're gonna have to divide both sides of the equation by negative 13.
그래서 우리는 방정식의 양변을 -13으로 나누어야 합니다.
32. 2:37 2:38
Now, what does the left-hand side become?
나, 워러저 렙탠 사이드 비커엄
33. 2:39 that's 2:42
34. 2:43 2:45
You multiply something times x, divide it by the something, you're just going to be left with an x.
35. 2:49 2:50
So the left-hand side just becomes an x.

36. 2:52 2:58
37. 3:00
.

[bdubj]

Although I'm done with Algebra, I do like to check back time to time for refresher. Your vids helped me out big time.

[stephanieparkinson]

How do you know when to add or subtract the numbers though?

[MMLauritsen]

Good video :) Could you do a video about probability calculus? :)

[FireStrikeKiki]

This helps so much, especially sence my math teacher is way too
fast

[jmills]

I dunno if it's been mentioned, or if the speaker/narrator/presenter (who's great, btw!) is doing it intentionally, but every so often he sounds like jeff goldblum in jurassic park and it's awesome

[jordandavis]

I paused the video then answered the question and got it right!

[Faatimahbaksh]

Anyone here in 2021 and has no idea what there teacher is saying so came to a video

[monimon]

I learnt more from a 4 minute video than a year in algebra and geometry (year 7 maths)

[Emily-itgx]

I don’t get it what if for the beginning step u could do +6 instead of -20?

[kleakodra]

My math teacher and the book doesn't explain how to solve the equation in this way. We actually do it with operational opposite...

[johnwelch]

Grate! now i can do beter in my skool!

[cambam]

I have this problem. Solve c=2 times pi times radius or r. Solve for r. How do I do this?

[bluesesnei]

any1 2020 struggling with their online math classes??

[aesthete-]

This method is hard just simply take 20 from the right side to left the sign changes so it becomes - 20 now you are left with - 7 x = 6 x - 6 - 20 and minus minus is Plus so you have - 26 now take the 6x from right to the left it will become - 6 x again - - is + so now it's - 13x = -26 now take -13 from the left side to the right its getting multiplied with X on left it will divide with 26 on right the - signs cancel out nd 26 divided by 13 is 2

[lpsStar]

What they forget to mention is that the variable is not always able to be on both sides, so afterward you should always plug in the number you get afterward, even if you are proud or satisfied with your work.