Writing and Graphing Inequalities - Free Educational videos for Students in K-12 | Lumos Learning

Writing and Graphing Inequalities - Free Educational videos for Students in k-12


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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