WEBVTT 00:00:00.641 --> 00:00:02.844 - [Voiceover] We have two inequalities here, the first one 00:00:02.844 --> 00:00:07.116 says that x plus two is less than or equal to two x. 00:00:07.116 --> 00:00:10.895 This one over here in I guess this light-purple-mauve color, 00:00:10.895 --> 00:00:15.057 is three x plus four is greater than five x. 00:00:15.057 --> 00:00:17.826 Over here we have four numbers and what I want to do in this 00:00:17.826 --> 00:00:21.507 video is test whether any of these four numbers 00:00:21.507 --> 00:00:24.884 satisfy either of these inequalities. 00:00:24.884 --> 00:00:26.957 I encourage you to pause this video and 00:00:26.957 --> 00:00:29.912 try these numbers out, does zero satisfy this inequality? 00:00:29.912 --> 00:00:32.353 Does it satisfy this one? Does one satisfy this one? 00:00:32.353 --> 00:00:33.708 Does it satisfy that one? 00:00:33.708 --> 00:00:35.797 I encourage you to try these four numbers out 00:00:35.797 --> 00:00:38.949 on these two inequalities. 00:00:38.949 --> 00:00:41.228 Assuming you have tried that, let's work 00:00:41.228 --> 00:00:42.957 through this together. 00:00:42.957 --> 00:00:47.935 Let's say, if we try out zero on this inequality 00:00:47.935 --> 00:00:50.616 right over here, let's substitute 00:00:51.523 --> 00:00:53.283 x with zero. 00:00:53.283 --> 00:00:57.554 So, we'll have zero plus two needs to 00:00:57.554 --> 00:01:02.329 be less than or equal to two times zero. 00:01:02.329 --> 00:01:04.071 Is that true? 00:01:04.071 --> 00:01:07.235 Well, on the left hand side, this is two needs to be 00:01:07.235 --> 00:01:09.965 less than or equal to zero. 00:01:09.965 --> 00:01:12.359 Is that true, is two less than or equal to zero? 00:01:12.359 --> 00:01:14.743 No, two is larger than zero. 00:01:14.743 --> 00:01:18.900 So this is not going to be true, this does not satisfy 00:01:20.304 --> 00:01:21.822 the left hand side inequality, let's see if it 00:01:21.822 --> 00:01:26.200 satisfies this inequality over here. 00:01:27.388 --> 00:01:31.936 In order to satisfy it, three times zero plus four 00:01:31.936 --> 00:01:35.651 needs to be greater than five times zero. 00:01:35.651 --> 00:01:39.495 Well three times zero is just zero, five times zero is zero. 00:01:39.495 --> 00:01:43.915 So four needs to be greater than zero, which is true. 00:01:43.915 --> 00:01:47.766 So it does satisfy 00:01:47.995 --> 00:01:50.459 this inequality right over here so zero 00:01:50.459 --> 00:01:53.525 does satisfy this inequality. 00:01:53.525 --> 00:01:55.233 Let's try out one. 00:01:56.902 --> 00:02:01.246 To satisfy this one, one plus two needs to be less than 00:02:01.246 --> 00:02:03.266 or equal to two. 00:02:03.518 --> 00:02:06.477 One plus two is three, is three less than or equal than two? 00:02:06.477 --> 00:02:09.200 No, three is larger than two. 00:02:09.576 --> 00:02:13.297 This does not satisfy the left hand inequality. 00:02:13.297 --> 00:02:16.600 What about the right hand inequality right over here? 00:02:17.218 --> 00:02:21.556 Three times one plus four needs to be greater than 00:02:21.556 --> 00:02:24.176 five times one. 00:02:24.176 --> 00:02:27.392 So three times one is three, plus four. 00:02:27.392 --> 00:02:31.926 So seven needs to be greater than five, well that's true. 00:02:31.926 --> 00:02:35.003 Both zero and one satisfy three x plus four is greater 00:02:35.003 --> 00:02:38.707 than five x, neither of them satisfy x plus two is less than 00:02:38.707 --> 00:02:41.502 or equal to two x. 00:02:41.502 --> 00:02:44.262 Now let's go to the two. 00:02:44.262 --> 00:02:46.701 I know it's getting a little bit unaligned, 00:02:46.701 --> 00:02:49.973 but I'll just do it all in the same color so you can tell. 00:02:49.973 --> 00:02:54.003 Let's try out two here, two plus two needs to be less than 00:02:54.003 --> 00:02:56.333 or equal to two times two. 00:02:56.474 --> 00:02:59.744 Four needs to be less than or equal to four. 00:02:59.744 --> 00:03:01.372 Well four is equal to four and it just has to be 00:03:01.372 --> 00:03:04.558 less than or equal, so this satisfies. 00:03:04.558 --> 00:03:07.439 This satisfies this inequality. 00:03:07.439 --> 00:03:10.200 What about this purple inequality? 00:03:10.200 --> 00:03:13.687 Let's see, three times two plus four needs to be 00:03:13.687 --> 00:03:17.064 greater than five times two. 00:03:17.064 --> 00:03:21.265 Three times two is six plus four is ten, 00:03:21.265 --> 00:03:24.266 needs to be greater than 10. 00:03:24.406 --> 00:03:27.090 10 is equal to 10, it's not greater than 10. 00:03:27.090 --> 00:03:31.394 It does not satisfy this inequality. 00:03:31.394 --> 00:03:34.814 If this was a greater than or equal to 00:03:34.814 --> 00:03:37.211 it would have satisfied but it's not. 00:03:37.211 --> 00:03:40.400 10 is not greater than 10. 00:03:40.528 --> 00:03:42.070 It would satisfy greater than or equal to 00:03:42.070 --> 00:03:43.869 because 10 is equal to 10. 00:03:43.869 --> 00:03:46.104 So two satisfies the left hand one but not 00:03:46.104 --> 00:03:47.833 the right hand one. 00:03:48.091 --> 00:03:50.200 Let's try out five. 00:03:52.486 --> 00:03:56.725 Five plus two needs to be less than or equal 00:03:56.725 --> 00:03:59.908 to two times five, once again everywhere we see 00:03:59.908 --> 00:04:02.033 an x, we replace it with a five. 00:04:02.207 --> 00:04:05.499 Seven needs to be less than or equal to 10. 00:04:05.499 --> 00:04:09.289 Which is absolutely true, seven is less than 10. 00:04:09.289 --> 00:04:11.662 So it satisfies less than or equal to. 00:04:11.662 --> 00:04:14.397 Five satisfies this inequality and what you're 00:04:14.397 --> 00:04:16.123 probably noticing now is that an inequality can 00:04:16.123 --> 00:04:18.180 have many numbers that satisfy. 00:04:18.180 --> 00:04:21.113 In fact they sometimes will have nothing that satisfies it 00:04:21.113 --> 00:04:23.546 and sometimes they might have an infinite number of 00:04:23.546 --> 00:04:26.721 numbers that satisfy it and you see that right over here. 00:04:26.721 --> 00:04:29.025 We're just testing out a few numbers. 00:04:29.025 --> 00:04:31.725 For this left one, zero and one didn't work, 00:04:31.725 --> 00:04:33.329 two and five did work. 00:04:33.329 --> 00:04:36.352 This right one, zero and one worked, two didn't work. 00:04:36.352 --> 00:04:38.246 Let's see what five does. 00:04:38.246 --> 00:04:41.616 In order for five to satisfy it, three times x. 00:04:41.616 --> 00:04:45.716 Now we're gonna try x being five. 00:04:45.716 --> 00:04:49.181 Three times five plus four needs to be greater than 00:04:49.181 --> 00:04:51.512 five times five. 00:04:51.512 --> 00:04:55.467 Three times five is fifteen, fifteen plus four is nineteen. 00:04:55.467 --> 00:04:59.704 Nineteen is to be greater than 25, it is not. 00:04:59.704 --> 00:05:02.603 So five does not satisfy 00:05:02.603 --> 00:05:05.466 this inequality right over here. 00:05:05.466 --> 00:05:08.067 Anyway, hopefully you found that fun.