Writing and Graphing Inequalities - By Anywhere Math
Transcript
00:0-1 | Welcome to anywhere , Math . I'm Jeff Jacobson . | |
00:01 | And today we're going to move on from solving equations | |
00:05 | and talk about inequality specifically how to write and graph | |
00:10 | inequalities . Let's get started . Okay , before we | |
00:32 | get to examples , let's talk about what exactly is | |
00:35 | in inequality . And inequality is just a mathematical sense | |
00:39 | . Is that compares expressions . Okay , notice uh | |
00:43 | if you look at the word inequality , you'll see | |
00:47 | equal in there , right ? Just like an equation | |
00:51 | , you can see equal in there , but before | |
00:53 | that you see the prefix in and the prefix in | |
00:58 | means not . So when inequality is not equal , | |
01:03 | okay , it's not an equation , it does not | |
01:08 | have an equal sign in it . Instead it has | |
01:11 | other symbols that mean uh different things . And we're | |
01:14 | gonna go over those symbols right now , here is | |
01:18 | example , number one , write the sentence as in | |
01:20 | inequality . So basically we're just translating these sentences into | |
01:24 | an inequality . Uh so let's read them just left | |
01:27 | to right . Like normal . A number C . | |
01:30 | Okay , so we're gonna see is less than that's | |
01:34 | important . We know what less than means if you | |
01:36 | don't look back at those notes from the what we | |
01:39 | just talked about Uh is less than -4 . So | |
01:42 | C is less than Mhm . Right . That looks | |
01:47 | like that negative form . There we go . We're | |
01:50 | done . See is less than -4 . Okay , | |
01:55 | let's look at the next one . Be a number | |
01:57 | K plus five is greater than or equal to . | |
02:04 | Okay . Okay , so let's see we've got a | |
02:07 | number K plus means we're adding we're adding five now | |
02:13 | is greater than or equal to OK . Greater than | |
02:18 | would be that . But because it says or equal | |
02:21 | to we have to have the line underneath . Okay | |
02:25 | , Greater than or equal to Hey , so that's | |
02:28 | going to look like that . Okay . Plus five | |
02:32 | is greater than or equal to eight now , the | |
02:35 | last +14 times the number Q is at most 16 | |
02:38 | . So we've got four times a number Q . | |
02:42 | So that would be four times Q . Which is | |
02:45 | just for Q . Is at most 16 Now at | |
02:51 | most . Let's think about that . If you say | |
02:54 | something is at most 16 ? Well can it be | |
02:58 | more than 16 ? No , it's at most . | |
03:00 | That means 16th . The maximum Uh it has to | |
03:04 | be 16 or less than that . So that would | |
03:07 | be for Q is less than You gotta think . | |
03:12 | Can it be can it be equal to 16 ? | |
03:16 | Yeah . At most 16 , that's the maximum it | |
03:18 | can be 16 , so it's less than or equal | |
03:21 | to 16 . Okay , For Q is less than | |
03:26 | or equal to 16 . This fork you cannot be | |
03:30 | more than 16 . That's at most what it is | |
03:34 | . Okay , Here's some more to try on your | |
03:38 | own . Okay , before we get to the next | |
03:49 | example , let's talk about what a solution to an | |
03:52 | inequality looks like or what it means . Just like | |
03:56 | an equation . A solution to an inequality is just | |
04:00 | a value that makes inequality true . Okay . Same | |
04:15 | thing as an equation . Right ? The only difference | |
04:18 | is , is that for inequalities most of the time | |
04:21 | you're going to have more than one solution ? Okay | |
04:24 | . If I say Uh x is going to be | |
04:27 | less than 6 ? Well , five is less than | |
04:30 | six . That would be a solution . Four is | |
04:33 | less than six . That's another solution . zero is | |
04:35 | less than six . That's the solution negative . A | |
04:38 | million is also less than six . So all of | |
04:41 | those would be solutions . So what we say is | |
04:44 | a solution set . A solution set is all solutions | |
04:55 | to and inequality . Okay . All the solutions together | |
05:02 | we call those the solutions set and most of the | |
05:05 | time . Well , well , show that using a | |
05:08 | graph . Okay , let's try another example . Alright | |
05:11 | , here we go . With example to tell whether | |
05:14 | the value is a solution of the inequality . So | |
05:17 | again , a solution to inequality means that would make | |
05:19 | the inequality true . And just like with equations uh | |
05:23 | to tell if a solution is or it's sorry to | |
05:27 | tell if a value is a solution , all we | |
05:29 | do is substitute . Okay , so expose one is | |
05:33 | greater than seven . We're testing whether X is equal | |
05:36 | to eight is a solution , so I'm just gonna | |
05:38 | substitute That eight in 4 x . Uh so that | |
05:43 | would be eight plus one is greater than 78 plus | |
05:46 | one is nine . The question is that greater than | |
05:51 | seven ? Yes , of course nine is greater than | |
05:53 | seven , so yes X equals eight is a solution | |
05:57 | to that inequality . Next seven . Y is less | |
06:01 | than 27 or testing the value four for ? Why | |
06:05 | ? If that's a solution so I'm gonna substitute that | |
06:08 | for And for what I get seven times four . | |
06:12 | Use your parentheses . Right ? That means multiplication . | |
06:15 | If I don't have them , it looks like 74 | |
06:18 | is less than 27 So seven times 4 is 28 | |
06:24 | . The question is that less than 27 ? Well | |
06:28 | , no , 28 is not less than 7.20 is | |
06:30 | greater than seven , which means no . Yeah . | |
06:34 | Why equals four is not a solution to that inequality | |
06:39 | . Okay . Here's some to try on your own | |
06:47 | . Okay , this is our last example uh graphic | |
06:50 | inequality . We've already written inequalities , translating them from | |
06:54 | sentences . We've looked at how to tell if a | |
06:57 | value is a solution now we're gonna grab And if | |
07:00 | you remember inequalities most of the time have more than | |
07:05 | one solution and I mentioned we call all the solutions | |
07:09 | together . The solution set in a great way to | |
07:13 | represent that solution set is by graphing . Okay , | |
07:17 | so we're gonna graph X is greater than two . | |
07:21 | Um to do that , notice we only have one | |
07:24 | variable . Sorry about that . We only have one | |
07:27 | variable . We're not going to be graphing on a | |
07:30 | coordinate plane because that has an X and Y . | |
07:33 | Value instead . This is gonna be one dimensional were | |
07:36 | graphing on a number line . So the first thing | |
07:39 | just draw your number line arrows at the ends because | |
07:43 | they go on , it goes in both directions forever | |
07:46 | . Um I always like to start with at least | |
07:50 | one number . I'm gonna start with zero right there | |
07:55 | and then put a line uh Mark where the other | |
07:59 | number is . So too is up here . Now | |
08:03 | the question is X is greater than two . Okay | |
08:07 | , that's all the values greater than two . It's | |
08:10 | not greater than or equal to two . It's just | |
08:12 | greater than two . So I don't include to to | |
08:15 | show that I don't include it . I put an | |
08:18 | open dot or an open circle . Okay . All | |
08:23 | the solutions are going to be greater than that . | |
08:25 | So what I do is I just draw an arrow | |
08:29 | point to all the numbers that are greater than two | |
08:32 | . That is my graph . That's it . So | |
08:36 | open circle , because it doesn't include two . It's | |
08:39 | just greater than uh and to the right , because | |
08:42 | that's all my numbers that are greater than two . | |
08:44 | Okay , let's look at B Why is less than | |
08:47 | or equal to four ? So again , I'm starting | |
08:50 | which is the number line ? I'm gonna have zero | |
08:53 | here for their this is why is less than or | |
09:00 | equal to . So four is also a solution . | |
09:03 | So I'm not going to have an open circle . | |
09:05 | I'm going to have a closed one or a closed | |
09:08 | dot . Okay ? You put it on the number | |
09:11 | line , by the way . We don't do it | |
09:12 | above the number line , right on there . Okay | |
09:15 | , Now the rest y is less than or equal | |
09:18 | to four . So all the numbers that are less | |
09:21 | than four , that would be to the left , | |
09:24 | so my arrow goes to the left and there's the | |
09:28 | graph of that inequality . Okay , here , somewhere | |
09:30 | to try on your own . Thank you so much | |
09:39 | for watching . And if you like this video , | |
09:40 | please subscribe . |
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