WEBVTT 00:00:00.283 --> 00:00:01.862 - [Voiceover] Let's give ourselves some practice 00:00:01.862 --> 00:00:03.650 solving equations. 00:00:03.650 --> 00:00:08.421 So let's say we had the equation 1/3 plus A 00:00:08.421 --> 00:00:10.905 is equal to 5/3. 00:00:10.905 --> 00:00:13.924 What is the A that makes this equation true? 00:00:13.924 --> 00:00:17.604 If I had 1/3 plus this A, what does A need to be 00:00:17.604 --> 00:00:22.604 in order for 1/3 plus that to be equal to 5/3? 00:00:23.873 --> 00:00:27.135 So there's a bunch of different ways of doing this, 00:00:27.135 --> 00:00:29.735 and this is one of the fun things about equations is 00:00:29.735 --> 00:00:32.835 there's no exactly one right way to do it. 00:00:32.835 --> 00:00:34.831 But let's think about what at least I think 00:00:34.831 --> 00:00:36.004 might be the simplest way. 00:00:36.004 --> 00:00:38.105 And before I work through anything, you should always try to 00:00:38.105 --> 00:00:40.891 pause the video, and do it on your own. 00:00:40.891 --> 00:00:45.891 So what I like to think about is can I have just my A 00:00:46.313 --> 00:00:47.892 on one side of the equation? 00:00:47.892 --> 00:00:49.536 And since it's already on the left-hand side, 00:00:49.536 --> 00:00:51.440 let's see if I can keep it on the left-hand side, 00:00:51.440 --> 00:00:53.831 but get rid of this 1/3 somehow. 00:00:53.831 --> 00:00:55.930 Well the easiest was I can think of getting rid of 00:00:55.930 --> 00:00:59.314 this 1/3 is to subtract 1/3 from the left-hand 00:00:59.314 --> 00:01:00.757 side of the equation. 00:01:00.757 --> 00:01:02.661 Now I can't just do that from the 00:01:02.661 --> 00:01:04.298 left-hand side of the equation. 00:01:04.298 --> 00:01:06.759 If 1/3 plus A is equal to 5/3, 00:01:06.759 --> 00:01:09.719 and if I just subtract 1/3 from the left-hand side, 00:01:09.719 --> 00:01:11.715 then they're not going to be equal anymore. 00:01:11.715 --> 00:01:13.699 Then this thing is going to be 1/3 less, 00:01:13.699 --> 00:01:15.059 which this thing isn't going to change. 00:01:15.059 --> 00:01:16.800 So then this thing on the left would become 00:01:16.800 --> 00:01:18.321 less than 5/3. 00:01:18.321 --> 00:01:20.862 So in order to hold the equality, whatever I do on the 00:01:20.862 --> 00:01:23.986 left-hand side I have to do on the right-hand side as well. 00:01:23.986 --> 00:01:26.819 So I have to subtract 1/3 from both sides. 00:01:26.819 --> 00:01:30.313 And if I do that, then on the left-hand side, 00:01:30.313 --> 00:01:32.391 1/3 minus 1/3, that's the whole reason why 00:01:32.391 --> 00:01:35.190 I subtracted 1/3 was to get rid of the 1/3, 00:01:35.190 --> 00:01:40.190 and I am left with A is equal to 5/3 minus 1/3, 00:01:41.829 --> 00:01:46.055 5/3 minus 1/3, 00:01:46.055 --> 00:01:49.762 minus 1/3, and what is that going to be equal to? 00:01:49.762 --> 00:01:53.268 I have five of something, in this case I have 5/3, 00:01:53.268 --> 00:01:55.893 and I'm gonna subtract 1/3. 00:01:55.893 --> 00:01:58.902 So I'm gonna be left with 4/3. 00:01:58.902 --> 00:02:03.902 So I could write A is equal to 4/3. 00:02:05.856 --> 00:02:07.482 And you could check to make sure that works. 00:02:07.482 --> 00:02:12.482 1/3 plus 4/3 is indeed equal to 5/3. 00:02:12.972 --> 00:02:14.853 Let's do another one of these. 00:02:14.853 --> 00:02:19.853 So let's say that we have the equation K minus eight 00:02:21.240 --> 00:02:24.920 is equal to 11.8. 00:02:24.920 --> 00:02:27.522 So once again I wanna solve for K. 00:02:27.522 --> 00:02:29.437 I wanna have just a K on the left-hand side. 00:02:29.437 --> 00:02:33.477 I don't want this subtracting this eight right over here. 00:02:33.477 --> 00:02:36.011 So in order to get rid of this eight, let's add eight 00:02:36.011 --> 00:02:36.795 on the left-hand side. 00:02:36.795 --> 00:02:38.095 And of course, if I do it on the left-hand side, 00:02:38.095 --> 00:02:40.278 I have to do it on the right-hand side as well. 00:02:40.278 --> 00:02:42.775 So we're gonna add eight to both sides. 00:02:42.775 --> 00:02:45.524 The left-hand side, you are substracting eight 00:02:45.524 --> 00:02:46.441 and then you're adding eight. 00:02:46.441 --> 00:02:47.615 That's just going to cancel out, 00:02:47.615 --> 00:02:49.761 and you're just going to be left with K. 00:02:49.761 --> 00:02:53.175 And on the right-hand side, 11.8 plus eight. 00:02:53.175 --> 00:02:58.175 Well, 11 plus eight is 19, so it's going to be 19.8. 00:02:58.758 --> 00:03:01.115 And we're done, and once again, what's neat about equations, 00:03:01.115 --> 00:03:03.413 you can always check to see if you got the right answer. 00:03:03.413 --> 00:03:07.803 19.8 minus eight is 11.8. 00:03:07.803 --> 00:03:10.542 Let's do another one, this is too much fun. 00:03:10.542 --> 00:03:15.542 Alright, so let's say that I had 5/13 is equal to 00:03:16.462 --> 00:03:20.259 T minus 6/13. 00:03:20.259 --> 00:03:22.362 Alright, this is interesting 'cause now I have my variable 00:03:22.362 --> 00:03:23.878 on the right-hand side. 00:03:23.878 --> 00:03:24.841 But let's just leave it there. 00:03:24.841 --> 00:03:27.545 Let's just see if we can solve for T by getting rid of 00:03:27.545 --> 00:03:29.263 everything else on the right-hand side. 00:03:29.263 --> 00:03:33.663 And like we've done in the past, if I'm subtracting 6/13, 00:03:33.663 --> 00:03:35.602 so why don't I just add it? 00:03:35.602 --> 00:03:37.424 Why don't I just add 6/13? 00:03:37.424 --> 00:03:38.776 I can't just do that on the right-hand side. 00:03:38.776 --> 00:03:41.110 Then the two sides won't be equal anymore, 00:03:41.110 --> 00:03:43.106 so I gotta do it on the left-hand side if I wanna 00:03:43.106 --> 00:03:45.289 hold the equality. 00:03:45.289 --> 00:03:47.007 So what happens? 00:03:47.007 --> 00:03:47.832 So what happens? 00:03:47.832 --> 00:03:50.466 On the left-hand side I have, 00:03:50.466 --> 00:03:52.126 let me give myself a little bit more space, 00:03:52.126 --> 00:03:56.615 I have 5/13 plus 6/13, 00:03:57.548 --> 00:04:01.880 plus 6/13 are equal to, 00:04:01.880 --> 00:04:03.702 are equal to... 00:04:03.702 --> 00:04:06.745 Well, I was subtracting 6/13, now I add 6/13. 00:04:06.745 --> 00:04:09.135 Those are just going to add to zero. 00:04:09.135 --> 00:04:12.943 6/13 minus 6/13 is just zero, so you're left with T. 00:04:12.943 --> 00:04:14.278 So T is equal to this. 00:04:14.278 --> 00:04:17.401 If I have 5/13 and I add to that 6/13, 00:04:17.401 --> 00:04:19.304 well I'm gonna have 11/13. 00:04:19.304 --> 00:04:24.018 So this is going to be 11/13 is equal to T, 00:04:24.018 --> 00:04:25.319 or I could write that the other way around. 00:04:25.319 --> 00:04:30.319 I could write T is equal to 11/13.