1 00:00:00,283 --> 00:00:01,862 - [Voiceover] Let's give ourselves some practice 2 00:00:01,862 --> 00:00:03,650 solving equations. 3 00:00:03,650 --> 00:00:08,421 So let's say we had the equation 1/3 plus A 4 00:00:08,421 --> 00:00:10,905 is equal to 5/3. 5 00:00:10,905 --> 00:00:13,924 What is the A that makes this equation true? 6 00:00:13,924 --> 00:00:17,604 If I had 1/3 plus this A, what does A need to be 7 00:00:17,604 --> 00:00:22,604 in order for 1/3 plus that to be equal to 5/3? 8 00:00:23,873 --> 00:00:27,135 So there's a bunch of different ways of doing this, 9 00:00:27,135 --> 00:00:29,735 and this is one of the fun things about equations is 10 00:00:29,735 --> 00:00:32,835 there's no exactly one right way to do it. 11 00:00:32,835 --> 00:00:34,831 But let's think about what at least I think 12 00:00:34,831 --> 00:00:36,004 might be the simplest way. 13 00:00:36,004 --> 00:00:38,105 And before I work through anything, you should always try to 14 00:00:38,105 --> 00:00:40,891 pause the video, and do it on your own. 15 00:00:40,891 --> 00:00:45,891 So what I like to think about is can I have just my A 16 00:00:46,313 --> 00:00:47,892 on one side of the equation? 17 00:00:47,892 --> 00:00:49,536 And since it's already on the left-hand side, 18 00:00:49,536 --> 00:00:51,440 let's see if I can keep it on the left-hand side, 19 00:00:51,440 --> 00:00:53,831 but get rid of this 1/3 somehow. 20 00:00:53,831 --> 00:00:55,930 Well the easiest was I can think of getting rid of 21 00:00:55,930 --> 00:00:59,314 this 1/3 is to subtract 1/3 from the left-hand 22 00:00:59,314 --> 00:01:00,757 side of the equation. 23 00:01:00,757 --> 00:01:02,661 Now I can't just do that from the 24 00:01:02,661 --> 00:01:04,298 left-hand side of the equation. 25 00:01:04,298 --> 00:01:06,759 If 1/3 plus A is equal to 5/3, 26 00:01:06,759 --> 00:01:09,719 and if I just subtract 1/3 from the left-hand side, 27 00:01:09,719 --> 00:01:11,715 then they're not going to be equal anymore. 28 00:01:11,715 --> 00:01:13,699 Then this thing is going to be 1/3 less, 29 00:01:13,699 --> 00:01:15,059 which this thing isn't going to change. 30 00:01:15,059 --> 00:01:16,800 So then this thing on the left would become 31 00:01:16,800 --> 00:01:18,321 less than 5/3. 32 00:01:18,321 --> 00:01:20,862 So in order to hold the equality, whatever I do on the 33 00:01:20,862 --> 00:01:23,986 left-hand side I have to do on the right-hand side as well. 34 00:01:23,986 --> 00:01:26,819 So I have to subtract 1/3 from both sides. 35 00:01:26,819 --> 00:01:30,313 And if I do that, then on the left-hand side, 36 00:01:30,313 --> 00:01:32,391 1/3 minus 1/3, that's the whole reason why 37 00:01:32,391 --> 00:01:35,190 I subtracted 1/3 was to get rid of the 1/3, 38 00:01:35,190 --> 00:01:40,190 and I am left with A is equal to 5/3 minus 1/3, 39 00:01:41,829 --> 00:01:46,055 5/3 minus 1/3, 40 00:01:46,055 --> 00:01:49,762 minus 1/3, and what is that going to be equal to? 41 00:01:49,762 --> 00:01:53,268 I have five of something, in this case I have 5/3, 42 00:01:53,268 --> 00:01:55,893 and I'm gonna subtract 1/3. 43 00:01:55,893 --> 00:01:58,902 So I'm gonna be left with 4/3. 44 00:01:58,902 --> 00:02:03,902 So I could write A is equal to 4/3. 45 00:02:05,856 --> 00:02:07,482 And you could check to make sure that works. 46 00:02:07,482 --> 00:02:12,482 1/3 plus 4/3 is indeed equal to 5/3. 47 00:02:12,972 --> 00:02:14,853 Let's do another one of these. 48 00:02:14,853 --> 00:02:19,853 So let's say that we have the equation K minus eight 49 00:02:21,240 --> 00:02:24,920 is equal to 11.8. 50 00:02:24,920 --> 00:02:27,522 So once again I wanna solve for K. 51 00:02:27,522 --> 00:02:29,437 I wanna have just a K on the left-hand side. 52 00:02:29,437 --> 00:02:33,477 I don't want this subtracting this eight right over here. 53 00:02:33,477 --> 00:02:36,011 So in order to get rid of this eight, let's add eight 54 00:02:36,011 --> 00:02:36,795 on the left-hand side. 55 00:02:36,795 --> 00:02:38,095 And of course, if I do it on the left-hand side, 56 00:02:38,095 --> 00:02:40,278 I have to do it on the right-hand side as well. 57 00:02:40,278 --> 00:02:42,775 So we're gonna add eight to both sides. 58 00:02:42,775 --> 00:02:45,524 The left-hand side, you are substracting eight 59 00:02:45,524 --> 00:02:46,441 and then you're adding eight. 60 00:02:46,441 --> 00:02:47,615 That's just going to cancel out, 61 00:02:47,615 --> 00:02:49,761 and you're just going to be left with K. 62 00:02:49,761 --> 00:02:53,175 And on the right-hand side, 11.8 plus eight. 63 00:02:53,175 --> 00:02:58,175 Well, 11 plus eight is 19, so it's going to be 19.8. 64 00:02:58,758 --> 00:03:01,115 And we're done, and once again, what's neat about equations, 65 00:03:01,115 --> 00:03:03,413 you can always check to see if you got the right answer. 66 00:03:03,413 --> 00:03:07,803 19.8 minus eight is 11.8. 67 00:03:07,803 --> 00:03:10,542 Let's do another one, this is too much fun. 68 00:03:10,542 --> 00:03:15,542 Alright, so let's say that I had 5/13 is equal to 69 00:03:16,462 --> 00:03:20,259 T minus 6/13. 70 00:03:20,259 --> 00:03:22,362 Alright, this is interesting 'cause now I have my variable 71 00:03:22,362 --> 00:03:23,878 on the right-hand side. 72 00:03:23,878 --> 00:03:24,841 But let's just leave it there. 73 00:03:24,841 --> 00:03:27,545 Let's just see if we can solve for T by getting rid of 74 00:03:27,545 --> 00:03:29,263 everything else on the right-hand side. 75 00:03:29,263 --> 00:03:33,663 And like we've done in the past, if I'm subtracting 6/13, 76 00:03:33,663 --> 00:03:35,602 so why don't I just add it? 77 00:03:35,602 --> 00:03:37,424 Why don't I just add 6/13? 78 00:03:37,424 --> 00:03:38,776 I can't just do that on the right-hand side. 79 00:03:38,776 --> 00:03:41,110 Then the two sides won't be equal anymore, 80 00:03:41,110 --> 00:03:43,106 so I gotta do it on the left-hand side if I wanna 81 00:03:43,106 --> 00:03:45,289 hold the equality. 82 00:03:45,289 --> 00:03:47,007 So what happens? 83 00:03:47,007 --> 00:03:47,832 So what happens? 84 00:03:47,832 --> 00:03:50,466 On the left-hand side I have, 85 00:03:50,466 --> 00:03:52,126 let me give myself a little bit more space, 86 00:03:52,126 --> 00:03:56,615 I have 5/13 plus 6/13, 87 00:03:57,548 --> 00:04:01,880 plus 6/13 are equal to, 88 00:04:01,880 --> 00:04:03,702 are equal to... 89 00:04:03,702 --> 00:04:06,745 Well, I was subtracting 6/13, now I add 6/13. 90 00:04:06,745 --> 00:04:09,135 Those are just going to add to zero. 91 00:04:09,135 --> 00:04:12,943 6/13 minus 6/13 is just zero, so you're left with T. 92 00:04:12,943 --> 00:04:14,278 So T is equal to this. 93 00:04:14,278 --> 00:04:17,401 If I have 5/13 and I add to that 6/13, 94 00:04:17,401 --> 00:04:19,304 well I'm gonna have 11/13. 95 00:04:19,304 --> 00:04:24,018 So this is going to be 11/13 is equal to T, 96 00:04:24,018 --> 00:04:25,319 or I could write that the other way around. 97 00:04:25,319 --> 00:04:30,319 I could write T is equal to 11/13.