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Pre-Algebra - 5.3: Inequalities

Added Feb 10, 2021 •

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What are the FOUR different Inequalities How to Translate an Inequality How to Write an Inequality How to Graph an Inequality

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quality so let's go look through this right here some of you guys have downloaded this right here so we got this water park and all that children under two are free children ages 2 to 11 you got to pay 12 but there's a Time adults they consider adult a twelve-year-old an adult at the waterpark yes they do cuz that's how they charging once you're 12 you're tall enough to ride the good ride what does the waterpark so good to get slime and then if you're old you're cheaper cuz old people don't really do much but you know they want to take the grandkids there so look at this right here with a true hero child be able to attend the water park for free and that's under sent a child under two a child too so that's the whole thing understanding if a child is 2 years old they're not free they got to pay $12 for $8 after 3 child under two is a child that is not two years old you could go one year and 11 months old one year 11 months in 20-something days that's still not 2 years old as long as the kid is under 2 for free but once they hit to they got to pay notice the difference twin underwear 2 under 2 vs 2 and above when would an adult when would an adult age 30 or pay less than $14 mission after so it's in the range adult is between 12 and 59 so in the range of 34 pay $14 but after 3 p.m. Dallas find the difference between difference mean subtraction so these are word problem find the difference find the difference between the Mission before 3 p.m. for a person age 59 to look at this 59 that is the last age you have to pay full price senior you're not old until you're 60 before 3 p.m. so before 3 p.m. 59 year old person pays $14 and a person 60 so before so yeah pay $4 more before 3 p.m. after I pay $3 more $2 more actually so these are problems the lot of guys messed up on on the ren star on the i-Ready is Lexile work the concert the simple you hearing me to strive it sounds simple but you guys actually doing it a lot of you guys loved on these are the things you got snubbed on it's not you guys messed up adding or subtracting its words and setting it up to something that you can calculate it's not even though Allconnect your reading your Lexile alright let's get on with this right an equality an inequality in a mathematical sentence that compares quantities that are not equal but inequalities can contain the symbol these are the four symbols we have less than greater than less than or equal no justice has not eaten are koalas are not equal even though it has an equal less than or equal to greater than or equal to its only is what it means the air quality is not only equal it could be less than or greater than Diego I blame you and not your friend stop writing in I don't depend on how much your fault writing an inequality for each sentence show you need to translate a sentence so the DVDs cost more than $15 so notice it's not the phrase is more that you know the DVDs cost more than $15 now everyone doesn't mess this up but this is the one that everyone read this is the literal translation now on your s back that state test that they always make you guys do they say all the ones that are the same and equal that you got this tonight here D is greater than 15 but you also need to know choose a color that's not there 15 is less than b you need to know both literal your DVDs cost more than the price of your DVDs is more $15 $15 is less than the cost of the DVDs so it's Lexile so inequalities were people mess up is knowing the is equivalent the equivalent even though their reverse people want to say it's the opposite that's not the opposite the opposite is he is less than -15 that's the opposite everyday is opposite so knowing both of these DVDs cost more than $15 $15 is not enough for the cost of the DVDs so you need to know both so this this second one is even more important than literally what it asked for so Dee pretty much words the DVD cost more than $15 d equals the cost of DVDs do we change them get a barrel plug in a variable and plug in your symbol D is greater than make it better little bit better not too much less glare so that matters a dog weighs less than 50 lb dog weighs 50 lb and this so this is one of the few times math we allow you use the word or anytime you guys on the test or you're not sure which is the right after I will always take out a whole point never a half a point never put when is it so your dog is less than 50 pounds well 50 lb is more than what your dog weighs so literal translation B is less than 50 450 is greater than all of them but for now for now I just want to decide alright so try these two out of your own type it in if you know it quiz the height requirement is bananer equal to 40 in greater than or equal to the speed limit is less than or equal to 35 miles an hour SO2 inequalities set those up you can't do this symbol that's behind there is actually the symbol there is a symbol I don't know how to get it there is like a an ALT you press alt and something her control something to get the symbol I just want the literal translation you don't need to give me both the somewhere in there you can type it in I don't know how to get to the special symbol I know if you're doing on the phone you do a hard pressed and it will come out but somewhere on Earth or you can actually do the equal it's alright it's alright alright so so the height the height requirement so so let's use the variable h each is what age is the height your height needs to be greater than or equal to 40 greater than equal to 40 that is better tallest you can be is 40 in as long as your 40in you can ride if your 39 in sorry your 41 in your good enough understand what this means you have to be at the released for call that's going around 40 is less than or equal to H if you want to sell me his wanted that but we I didn't ask for that you did not need it but I'm just writing it down so 40 you need to be at least 40 the height needs to be greater than or equal to 41 speed limit is less than or equal to 35 miles an hour less than you could anything faster than 35 miles are you going to get a ticket I hate the variable s cuz sometimes it looks like the number 5 what's the score with s so you can cut my S count to 5 so s is less than HoopsHype Oklahoma s is less than or equal to 35 that's simple but I'm especially for translation problem on your test at all I'm just going to make you do free stuff all right but vocabulary words so let's go look at these are key less than well is less than so right here and they messed with you didn't have the word is cuz less than or is that she does is greater than is less than cuz the whole thing is what is this song let me write translate something else don't get confused a number less 48 less than a number is 72 so look at this one right here you have to read it this is Lexa versus this they literally say and that's why you got to read requirement is greater than or equal to know where it is it should stand for equal but is is a separator liquor I hear the word is right here's a separate 48 less than a number is to the word is in this case means equal 7248 less than a number it's not the symbol less than it is -48 - 40 and -48 so in this case less than is subtraction but they use the phrase is less than even though up here we have the dog DVD the cost the DV because the DVD cost is you got to read the word is known as they don't have the word is in there same thing a dog's weight and dog weighs less than 15 it's not subtraction reading you know it's less so watch out and take your time on these inequalities that's where people mess up so easily just by translating it when they're nice Wendy's inequalities things are nice they have the word is if it is less than noticed they don't always use the word less Fiorentina your dad more than it sees you know this comedic Lines by here this is just a short list there is a bigger list and there's a glare but it's not clear right and then we send our equal 2 is less than or equal to look at this one is no more then it can't be greater than is at most even though here's thing is less than you hear the word when you hear the word most think big but no that's the maximum it can be if this is as high as it can go music to be less that's why you want to have Lexa look at this greater than or equal to is no less than not less than it has to be bigger than is at least you got to be at least 40 lb to ride the smallest it could be but it could be greater lexology for these things notice that less than equal less than equal to and greater than and equal to or in combination of less than or the greater than spoke with part of the symbol for equal better so these are only some when you come across this stuff when you read it on the state test I'm going to say they're easy but take a little bit of extra time to read through it these are free questions free problems that you should get right that you do not want to throw away and you have us do take it me I messed up don't my mistakes that's become a teacher become data I have a bill read this you must be at least 18 years old to vote write an inequality to describe the situation so got to be at least 18 years old to vote so this one right the state test is not great at the state test do the state test is on your record it doesn't count towards your grade but it does list it doesn't list where does list what what level you're at on your permanent record so each year that you have to take it you know you don't get a letter grade for it but in your record there's a thing that says it has a section 4 best test right here it just says what you're at so what they wouldn't what people would people use it for is like a hey this person got a man they tested it man just be lazy who are the other way around this person got an A in this class but tested below this class has either easy the teacher is super easy or hey that use other things on that test or other things so that's what the state test thing is for is for for for us as the teachers and whatnot in the school we who's at the place you in classes we check to see if you're correctly placed in a cuz if you got an A but you tested super below like maybe it was only because the teacher was super easy so I don't think put them in the advanced class versus the other way around if you tested Super Bass but you got like a d or another that is full of just not challenge lazy so we're going to put them in a more advanced class to get their motor running inspire that's how we use the test score making me say the word grade I said it but yet we real grade at per se showboating your vote if you're going to vote your age needs to be here's the thing. I know where you got to think this is the voting age your voting age needs to be greater than or equal to 18 that's why you always want to talk this stuff you know you need to be at least equal to 18 no start-up no one mess that up but you got to think the voting the b stands for the voting age of the person don't focus on number yes so you're voting age needs to be greater than or equal to 18 think about this couple of you guys I get it but here you still at least have the equal symbol but you had the key is less than or equal to 80 this part right here at least I would at least I give you one point for setting it up you just had the wrong inequality symbol the voting age is less than or equal to 18 so this right here represents the egg when we get two variables plug in a number to test can a number you want the number that true give me a number less than or equal to 18 so if I am 7 years old less than or equal to 18 I can vote no where did I get 7 from someone just type it I just made it up I put in a number that fits this and I ask myself does that fit that statement that's Lexile right there by the number right here looking for number greater than 18 70 Mindy is greater than or equal to what's the word or as long as it fits one criteria is 70 greater than 18 yes is 70 equal I know but it is so it's in its able to fit in that's why it's greater than or equal to if it's a team is 18 greater than 18 18 is equal to 18 it just needs to fit one of these as long as true for one of these it's true for the whole thing that's why I inequalities mess people up that's the only difference in stuff we've been doing yes so if I'm 17 is greater than 18 I can vote if I am 7 years old 7 is not greater than 18 they chose a 4-H I chose be like many of you did be has to be greater than or equal to 18 do you got him or here look at this one you have to be you have to be at least at least 18 te bote you have to be at least 18 the vote that would be this sentence right here you're voting age is greater than or equal to 18 you have to be at least at least 18 to vote with this sentence right here so show me how to write the sentences using these phrases will help you understand this sorry take the 2nd right here try to do this one on your own a student must have at least 10 hours of instructor insisted driving time to pass the course write an inequality to describe this situation ever said a student must have at least 7 hours of instructor at Vista driving time to pass write an inequality to describe the situation plug-in number plug in numbers I'm going to do that in the second I set that up set up your own thank you all right what's going on so think about it you need at least 10 hours so you have to have this the equal sides are you need to have at least an hour so I need to have at least at the very least 10 hours but so low free number that makes it true I have 12 hours that's that's more than enough so 10 is less than 12 give me a another number 1510 is less 15 that is true but instead of 12 and 15 let me in so notice when I did hear I just I found I made up numbers that make it true and now I want to but doesn't equal but it could be 10 is less than or equal to 10 so I fit in that cuz it could be at least 10 so on this side instead of numbers now I have a very hours 10 is less than or equal to the number of hours but if the opposite some of you guys always like to have the variable first the hours I have need to be greater than or equal to 10 flip it around 12 is is greater than love is greater than myself that's why I use the number 15 is greater than 10 and has to be greater than or equal to 10 so I switch this side to my variable this is called modeling what I'm doing unplugging and number to model something that I can grasp an idea model it if you need to model it and then replace it this is a concept I didn't catch on to till super my math career some of these guys are going to start doing it which is fine Marlatt model it so you can see it to you start to understand what is asking for all right next one let's go with this song example inequalities with variables are open sentences when the variable is in an open sentence is replaced with a number the inequality may be true or false that's why you want to test is a test scenario so look at this so we can do a and b 2T + 8 is greater than 7 for so a semicolon mean for your testing out is this true when she is equal -1 so we have this right here 2T + 8 is greater than 7 true or false is also asking when T is equal to -1 so 2 * -1 yes I always put parentheses when I substitute it's because if you don't have parentheses many of you will mess things up to -1 instead of 2 * -1 safe thing to do getting put parentheses around you substitute ? Is that greater than so who * -1 is to -2 plus a negative is that -2 + 8 that's 6 6 is greater than 7 know it is false and that's all you do at least give you these right here true or false he is p - B2 is less than or equal to negative 2 key 42 is less than or equal to negative 2 and in place of P I'm going to put the number 40 40 - 42 is negative 2 less than or equal to negative 2 -2 is not less than -2 but because we have this equal symbol it allows us to be true less than or equal -2 equals -2 it's not less than but because we have this right here and makes it true someone said what if the equal thing is not under there then it's false let's clarify so this statement is true but this statement would be false -2 is not less than 2 so this little equal symbol under there important less than or equal to these aren't less than but they are equal that's what makes this true but if you do not have this thing -2 is not less than that who to their equal so this one's false so try these two right here 3A and 3B 3 + x less than or equal to 12 or x equals 6 3D y - 7 is less than 10 4y equals 17 this is a different problem which reminds me of the go on a beside thing II try these. make sure you know what you're doing all of you in this class that are not getting a c or higher you're too smart to not do that next are they're going to put you still in an advanced class because of your scores on your test that you've been taking your red star I ready you don't pass my class English and science you guys have heard your friends in your other classes they are going to hold students back even though your Advanced you shouldn't be held Pastor repeat the 7th grade I don't see you guys writing there's a reason why start turning in work turn in late work start getting some points give me a reason to give you guys a b and a I don't want to but I would rather give you guys a c then the other grades ask questions for the weekend 3 plus is less than or equal to negative 12 x equals 6 you do not need to rewrite this problem you do not need to rewrite this just in 3 + what is X x is 6 less than or equal 212 3 + 6 is 9 9 is less than or equal to 12 so that is true now this right here y - 7 is less than 10 for Weigel's I don't need to write y 17 + 17 + 17 - 7 is less than 1017 - 710 is less than 10 that is false all we're doing is simplifying the expression yeah that's the whole thing how do you do that time I don't know how to do the equal sign equal less than equal have the less than or equal there's a way to press pulse so next time you guys going to Google or or if you have Microsoft Office go and can you type in some fine draw drop down menu for symbols insert symbol when you open the insert symbols you can actually find that symbol in there but there's also a shortcut those are called hotkeys result in a combination of two digit or three digit number you can actually get that number to pop up I don't know how to do that but I get what you're trying to do thank you next line yes we're moving through the super fast so now we're graphing graphing there here's a thing the book shows one way but I'm going to show you that on the East Coast they show another way why East Coast Forget You European countries Asian countries that actually two ways to show these so right here graph each inequality on a number line so all the number line there is no variable it's dead assemble listen to this when graphing inequalities inequalities are graphs and open. Means the number is not included open. Open circle which we call it is less than or equal to and a closed. is solid. Means it is less than or equal to imma show you other symbols that are being used I'll do this one first right here so noticed there's no equal sign so we need to open circle all it is on a number line so here's a number line most people like to put the Bro in the minute you don't have to I'm going to do it two ways without a zero and a zero so I have the number is at 6:06 is right here I know it's on the Plaza so I'm just put that as 6 right here because it does not include 6 this is what they mean as an open circle so that the number you have to have a closed. Or an open sore because it's not equal open the variable is the arrow direction that it needs and this is where you test out give me a number before six and a number after six 5 and 7 so the number before 6 and 5 the number after 6 is 7 you graph the trueway what is this 5 is less than 5 is greater than 6 that's false 7 is greater than 6 that's true so you grass the true side the arrow is the variable the arrow represents a now do I have to put the zero there no I could just do this that's the cheap lazy way and I would still get both but I'm not going to give this right here there's not working about guess either know it or you don't yes it needs to be Hollow and I'm going to show you I'm going to come back to this so let's show a difference were here notice this right here as the x is less than or equal to so let's do this right here I'm going to leave a little bit of space cuz imma show you another way to graph these so in this case we have X is less than or equal to negative one so let's just do the lazy way so I'm not going to put the zero down at negative one hears negative one at negative instead of an open circle because it includes -1 you fill it in that's the difference this does not include 6 this includes negative one so open circle closed. That's what they mean now I'm going to put a number before and after 0 + -2 is 0 is 0 less than negative 100 is -2 less than -1 yes less than is always on the left so this is the sign on graphing and so they got that to notice a difference open circle closed. so always find your number on the number line first pretty much what I did II open app that number is it open or closed and the next thing the last thing you do is your arrow now I'm going to show you a the way that other countries have done this to so it's the similar thing everything's the same except for the symbols open or closed now if it's open the use of parentheses want to hear Let me just drive the number first so at 6 they have a parentheses and they draw the arrow going this way that's another symbol I want you guys to do the open circle and closed. But I'm showing you the other way that this do it for not including the number at 6th and have a close parentheses and they are going through it when it's included though let's go negative one right here when it's concluded it's a bracket instead of United's that right there and then the arrow the only difference the only difference so know that used to exist for other places for some reason it's America that does the other countries use a right but sometimes on test they make some back and forth I heard that the ACT uses both of these they switch back and forth I don't know I've never taken the ACT is another version is not a version it's another test like the SAT so all these right here the red ones no don't do them I'm just showing it to you stick with open circle closed. That's what I want you to use try these three on your out there on your own you're nothing you just got to answer that's why I'm not giving these on the test but make sure you know what you're doing so for a b and c give me those tomorrow cuz you're going to have to rafter answers tomorrow. Tomorrow they're next class you're going to have to know how to do this for an answer and you're going to have more the work itself if you just need to know how to graph so this will literally be your work part of your work in another type of problem but for a b and c get those done and then we can move on to 5 take me to Amazon. Super nice yes and again yes it's super easy like you said thank you for typing that down I didn't know that this is not going to be on your test but in the process will be part of their phone so let's look at that ignore the negative when I should have folded it some more try not to waste paper all right yes I got it I got a good job so arrows is greater than x is less than 5 so the are in pretty much forget the variable find the number be lazy here's five because there's no what sign is an open circle and hair all you got to do is test number before that is 6 after that is 7 which number that's no 6 it's at 4 4 and 7/3 are numbers before and after give me which one is true for isn't in 575 so that is true that's how simple it is X is not greater than or equal to -2 so here is -2 + at -2 a. Instead of a circle open circle number before that is 0 number after that let's go negative 7 -7 is not greater than greater than is always towards the right 0 is greater than 8 and then right here we're at zero and because there's no equal sign another it's open a number greater than 0 is 1 u.s. Bank what if I give you a graph write an inequality for it right here's the thing on the S back the ex you want both both inequalities it's all right here we got this stuff right here write an inequality for the graph they don't give you variable and so on the S back test you need to know that they're going to use whatever variable they decide most of us like to stick with the variable X but we don't have that let's not do it I'm going to use Q so the arrow represent in the arrow represent your variable you have to remember the arrow represent Arrow represents your verbal cue what is what what direction is my arrow going Raider that Q is greater than that because it's not open there's no equal sign to Q plug in a number that's true 3466 is greater than 2 but you need to go the other way around 2 or two is less than Q I didn't trust you you chose X and it doesn't matter cuz that's the thing about the you can choose whatever variable you want unless they choose for you that's why I'm just a test herbal choice just because and that's the thing that pissed that if I chose to but they have W did I do something wrong that you start over it's a variable you know try these Sahara dust and open circle blah blah blah X is greater than 2 she was greater than 2 or 2 is less than Q try 5A and 5B on your own make sure do you know what you are doing 5A 5B thank you super easy I know right yeah wait what do you mean open. And Clip open. Right here she see that right there notice it's not solid you can see through the num this this right that's a close. That means that negative that too is not included it's not equal to where has this right here is our clothes that -3 is included as part of the answer no other parents open Mega 2 is not included as your answer you have to grasp it at -2 but it doesn't include it's like that thing if you're under to you get to go into water park for free but if you're 2 years old now you have to pay it's all good right direction they're all right watch out it's not a variable equation and is not so literally all right so remember the arrow represent your variable let's just say the arrow represents your variable what is my variable to the number the variable is growing higher is greater than my number my number is -3 because it's a closed Circle closed. It includes the equal sign X is greater than or equal to negative 3 that's what it means to be closed when its open here let's do this let's do this for when it's open all right let's do my variable my variable what is my variable to the number it's going this way so it's less than but since it's open there's no equal sign thing under there and then I just put the number so it's just we're not doing a variable set up symbol so it's just a yes negative or negative 3 less than or equal to X yes I get what you're saying sorry my fault I didn't get it be is -2 is better than x thank you I didn't see that put a parentheses after the a I would have been all right vs be this is the if you guys just have this answer I'm perfectly happy with that but I do need you to understand that there are there is a second way for everything every an equality has a second way of writing it notice how things are just slipped around and that is key if this will help you understand tomorrow's but not tomorrow but next fast alright so

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Pre-Algebra - 5.3: Inequalities

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