[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.28,0:00:01.86,Default,,0000,0000,0000,,- [Voiceover] Let's give\Nourselves some practice
Dialogue: 0,0:00:01.86,0:00:03.65,Default,,0000,0000,0000,,solving equations.
Dialogue: 0,0:00:03.65,0:00:08.42,Default,,0000,0000,0000,,So let's say we had\Nthe equation 1/3 plus A
Dialogue: 0,0:00:08.42,0:00:10.90,Default,,0000,0000,0000,,is equal to 5/3.
Dialogue: 0,0:00:10.90,0:00:13.92,Default,,0000,0000,0000,,What is the A that makes\Nthis equation true?
Dialogue: 0,0:00:13.92,0:00:17.60,Default,,0000,0000,0000,,If I had 1/3 plus this\NA, what does A need to be
Dialogue: 0,0:00:17.60,0:00:22.60,Default,,0000,0000,0000,,in order for 1/3 plus\Nthat to be equal to 5/3?
Dialogue: 0,0:00:23.87,0:00:27.14,Default,,0000,0000,0000,,So there's a bunch of\Ndifferent ways of doing this,
Dialogue: 0,0:00:27.14,0:00:29.74,Default,,0000,0000,0000,,and this is one of the fun\Nthings about equations is
Dialogue: 0,0:00:29.74,0:00:32.84,Default,,0000,0000,0000,,there's no exactly one right way to do it.
Dialogue: 0,0:00:32.84,0:00:34.83,Default,,0000,0000,0000,,But let's think about\Nwhat at least I think
Dialogue: 0,0:00:34.83,0:00:36.00,Default,,0000,0000,0000,,might be the simplest way.
Dialogue: 0,0:00:36.00,0:00:38.10,Default,,0000,0000,0000,,And before I work through\Nanything, you should always try to
Dialogue: 0,0:00:38.10,0:00:40.89,Default,,0000,0000,0000,,pause the video, and do it on your own.
Dialogue: 0,0:00:40.89,0:00:45.89,Default,,0000,0000,0000,,So what I like to think\Nabout is can I have just my A
Dialogue: 0,0:00:46.31,0:00:47.89,Default,,0000,0000,0000,,on one side of the equation?
Dialogue: 0,0:00:47.89,0:00:49.54,Default,,0000,0000,0000,,And since it's already\Non the left-hand side,
Dialogue: 0,0:00:49.54,0:00:51.44,Default,,0000,0000,0000,,let's see if I can keep\Nit on the left-hand side,
Dialogue: 0,0:00:51.44,0:00:53.83,Default,,0000,0000,0000,,but get rid of this 1/3 somehow.
Dialogue: 0,0:00:53.83,0:00:55.93,Default,,0000,0000,0000,,Well the easiest was I can\Nthink of getting rid of
Dialogue: 0,0:00:55.93,0:00:59.31,Default,,0000,0000,0000,,this 1/3 is to subtract\N1/3 from the left-hand
Dialogue: 0,0:00:59.31,0:01:00.76,Default,,0000,0000,0000,,side of the equation.
Dialogue: 0,0:01:00.76,0:01:02.66,Default,,0000,0000,0000,,Now I can't just do that from the
Dialogue: 0,0:01:02.66,0:01:04.30,Default,,0000,0000,0000,,left-hand side of the equation.
Dialogue: 0,0:01:04.30,0:01:06.76,Default,,0000,0000,0000,,If 1/3 plus A is equal to 5/3,
Dialogue: 0,0:01:06.76,0:01:09.72,Default,,0000,0000,0000,,and if I just subtract 1/3\Nfrom the left-hand side,
Dialogue: 0,0:01:09.72,0:01:11.72,Default,,0000,0000,0000,,then they're not going\Nto be equal anymore.
Dialogue: 0,0:01:11.72,0:01:13.70,Default,,0000,0000,0000,,Then this thing is going to be 1/3 less,
Dialogue: 0,0:01:13.70,0:01:15.06,Default,,0000,0000,0000,,which this thing isn't going to change.
Dialogue: 0,0:01:15.06,0:01:16.80,Default,,0000,0000,0000,,So then this thing on\Nthe left would become
Dialogue: 0,0:01:16.80,0:01:18.32,Default,,0000,0000,0000,,less than 5/3.
Dialogue: 0,0:01:18.32,0:01:20.86,Default,,0000,0000,0000,,So in order to hold the\Nequality, whatever I do on the
Dialogue: 0,0:01:20.86,0:01:23.99,Default,,0000,0000,0000,,left-hand side I have to do on\Nthe right-hand side as well.
Dialogue: 0,0:01:23.99,0:01:26.82,Default,,0000,0000,0000,,So I have to subtract 1/3 from both sides.
Dialogue: 0,0:01:26.82,0:01:30.31,Default,,0000,0000,0000,,And if I do that, then\Non the left-hand side,
Dialogue: 0,0:01:30.31,0:01:32.39,Default,,0000,0000,0000,,1/3 minus 1/3, that's the whole reason why
Dialogue: 0,0:01:32.39,0:01:35.19,Default,,0000,0000,0000,,I subtracted 1/3 was\Nto get rid of the 1/3,
Dialogue: 0,0:01:35.19,0:01:40.19,Default,,0000,0000,0000,,and I am left with A is\Nequal to 5/3 minus 1/3,
Dialogue: 0,0:01:41.83,0:01:46.06,Default,,0000,0000,0000,,5/3 minus 1/3,
Dialogue: 0,0:01:46.06,0:01:49.76,Default,,0000,0000,0000,,minus 1/3, and what is\Nthat going to be equal to?
Dialogue: 0,0:01:49.76,0:01:53.27,Default,,0000,0000,0000,,I have five of something,\Nin this case I have 5/3,
Dialogue: 0,0:01:53.27,0:01:55.89,Default,,0000,0000,0000,,and I'm gonna subtract 1/3.
Dialogue: 0,0:01:55.89,0:01:58.90,Default,,0000,0000,0000,,So I'm gonna be left with 4/3.
Dialogue: 0,0:01:58.90,0:02:03.90,Default,,0000,0000,0000,,So I could write A is equal to 4/3.
Dialogue: 0,0:02:05.86,0:02:07.48,Default,,0000,0000,0000,,And you could check to\Nmake sure that works.
Dialogue: 0,0:02:07.48,0:02:12.48,Default,,0000,0000,0000,,1/3 plus 4/3 is indeed equal to 5/3.
Dialogue: 0,0:02:12.97,0:02:14.85,Default,,0000,0000,0000,,Let's do another one of these.
Dialogue: 0,0:02:14.85,0:02:19.85,Default,,0000,0000,0000,,So let's say that we have\Nthe equation K minus eight
Dialogue: 0,0:02:21.24,0:02:24.92,Default,,0000,0000,0000,,is equal to 11.8.
Dialogue: 0,0:02:24.92,0:02:27.52,Default,,0000,0000,0000,,So once again I wanna solve for K.
Dialogue: 0,0:02:27.52,0:02:29.44,Default,,0000,0000,0000,,I wanna have just a K\Non the left-hand side.
Dialogue: 0,0:02:29.44,0:02:33.48,Default,,0000,0000,0000,,I don't want this subtracting\Nthis eight right over here.
Dialogue: 0,0:02:33.48,0:02:36.01,Default,,0000,0000,0000,,So in order to get rid of\Nthis eight, let's add eight
Dialogue: 0,0:02:36.01,0:02:36.80,Default,,0000,0000,0000,,on the left-hand side.
Dialogue: 0,0:02:36.80,0:02:38.10,Default,,0000,0000,0000,,And of course, if I do\Nit on the left-hand side,
Dialogue: 0,0:02:38.10,0:02:40.28,Default,,0000,0000,0000,,I have to do it on the\Nright-hand side as well.
Dialogue: 0,0:02:40.28,0:02:42.78,Default,,0000,0000,0000,,So we're gonna add eight to both sides.
Dialogue: 0,0:02:42.78,0:02:45.52,Default,,0000,0000,0000,,The left-hand side, you\Nare substracting eight
Dialogue: 0,0:02:45.52,0:02:46.44,Default,,0000,0000,0000,,and then you're adding eight.
Dialogue: 0,0:02:46.44,0:02:47.62,Default,,0000,0000,0000,,That's just going to cancel out,
Dialogue: 0,0:02:47.62,0:02:49.76,Default,,0000,0000,0000,,and you're just going to be left with K.
Dialogue: 0,0:02:49.76,0:02:53.18,Default,,0000,0000,0000,,And on the right-hand\Nside, 11.8 plus eight.
Dialogue: 0,0:02:53.18,0:02:58.18,Default,,0000,0000,0000,,Well, 11 plus eight is 19,\Nso it's going to be 19.8.
Dialogue: 0,0:02:58.76,0:03:01.12,Default,,0000,0000,0000,,And we're done, and once again,\Nwhat's neat about equations,
Dialogue: 0,0:03:01.12,0:03:03.41,Default,,0000,0000,0000,,you can always check to see\Nif you got the right answer.
Dialogue: 0,0:03:03.41,0:03:07.80,Default,,0000,0000,0000,,19.8 minus eight is 11.8.
Dialogue: 0,0:03:07.80,0:03:10.54,Default,,0000,0000,0000,,Let's do another one,\Nthis is too much fun.
Dialogue: 0,0:03:10.54,0:03:15.54,Default,,0000,0000,0000,,Alright, so let's say that\NI had 5/13 is equal to
Dialogue: 0,0:03:16.46,0:03:20.26,Default,,0000,0000,0000,,T minus 6/13.
Dialogue: 0,0:03:20.26,0:03:22.36,Default,,0000,0000,0000,,Alright, this is interesting\N'cause now I have my variable
Dialogue: 0,0:03:22.36,0:03:23.88,Default,,0000,0000,0000,,on the right-hand side.
Dialogue: 0,0:03:23.88,0:03:24.84,Default,,0000,0000,0000,,But let's just leave it there.
Dialogue: 0,0:03:24.84,0:03:27.54,Default,,0000,0000,0000,,Let's just see if we can\Nsolve for T by getting rid of
Dialogue: 0,0:03:27.54,0:03:29.26,Default,,0000,0000,0000,,everything else on the right-hand side.
Dialogue: 0,0:03:29.26,0:03:33.66,Default,,0000,0000,0000,,And like we've done in the\Npast, if I'm subtracting 6/13,
Dialogue: 0,0:03:33.66,0:03:35.60,Default,,0000,0000,0000,,so why don't I just add it?
Dialogue: 0,0:03:35.60,0:03:37.42,Default,,0000,0000,0000,,Why don't I just add 6/13?
Dialogue: 0,0:03:37.42,0:03:38.78,Default,,0000,0000,0000,,I can't just do that\Non the right-hand side.
Dialogue: 0,0:03:38.78,0:03:41.11,Default,,0000,0000,0000,,Then the two sides won't be equal anymore,
Dialogue: 0,0:03:41.11,0:03:43.11,Default,,0000,0000,0000,,so I gotta do it on the\Nleft-hand side if I wanna
Dialogue: 0,0:03:43.11,0:03:45.29,Default,,0000,0000,0000,,hold the equality.
Dialogue: 0,0:03:45.29,0:03:47.01,Default,,0000,0000,0000,,So what happens?
Dialogue: 0,0:03:47.01,0:03:47.83,Default,,0000,0000,0000,,So what happens?
Dialogue: 0,0:03:47.83,0:03:50.47,Default,,0000,0000,0000,,On the left-hand side I have,
Dialogue: 0,0:03:50.47,0:03:52.13,Default,,0000,0000,0000,,let me give myself a\Nlittle bit more space,
Dialogue: 0,0:03:52.13,0:03:56.62,Default,,0000,0000,0000,,I have 5/13 plus 6/13,
Dialogue: 0,0:03:57.55,0:04:01.88,Default,,0000,0000,0000,,plus 6/13 are equal to,
Dialogue: 0,0:04:01.88,0:04:03.70,Default,,0000,0000,0000,,are equal to...
Dialogue: 0,0:04:03.70,0:04:06.74,Default,,0000,0000,0000,,Well, I was subtracting\N6/13, now I add 6/13.
Dialogue: 0,0:04:06.74,0:04:09.14,Default,,0000,0000,0000,,Those are just going to add to zero.
Dialogue: 0,0:04:09.14,0:04:12.94,Default,,0000,0000,0000,,6/13 minus 6/13 is just\Nzero, so you're left with T.
Dialogue: 0,0:04:12.94,0:04:14.28,Default,,0000,0000,0000,,So T is equal to this.
Dialogue: 0,0:04:14.28,0:04:17.40,Default,,0000,0000,0000,,If I have 5/13 and I add to that 6/13,
Dialogue: 0,0:04:17.40,0:04:19.30,Default,,0000,0000,0000,,well I'm gonna have 11/13.
Dialogue: 0,0:04:19.30,0:04:24.02,Default,,0000,0000,0000,,So this is going to be\N11/13 is equal to T,
Dialogue: 0,0:04:24.02,0:04:25.32,Default,,0000,0000,0000,,or I could write that\Nthe other way around.
Dialogue: 0,0:04:25.32,0:04:30.32,Default,,0000,0000,0000,,I could write T is equal to 11/13.