Solving Rational Inequalities

[tillathahun]

really great directions clear and easy to understand- thanks for helping me with my midterm tomorrow man

[guitarheroloverr]

dude i would do anything for you to be my algebra 2 tutor :-0

[AflakAttack]

I have my Pre-Calc finals tomorrow! I got so used to just flying by math classes in elementary school and middle school and the first 2 years of high school have fucked me over because I got so used to not having to do my homework! Thanks so much man honestly when I search a math video on YouTube I don't watch it unless it is yours! :D

[patrickJMT]

@AflakAttack good luck on the final!

[stratoge]

Man you know my math teacher makes these rational inequalities all complicated. with many exponents, and canceling alot if they don't matter on making the equation positive or negative

[Assassin7z]

thanks that was helpful.

[iScoutYourAss]

dude u make more sence then my math teacher...

[MizMimiCullen]

This videos are the best study aids ever..

[nouh220200]

Why do I test points ? what is the purpose ?

[patrickJMT]

@nouh220200 to determine which intervals of numbers work and which do not.

[BurnSpangler]

awesome! thanks so much :) xox

[foolintherain100]

These videos are great! I have a test tomorrow, and FINALLY understand this XD!

[wedontknow]

The sign changing when it comes to writing the intervals is really confusing me. If its greater-less than or equal to but the parenthesis are the answers???

[lavendretta]

what if the denominator is a quadratic function?

[patrickJMT]

@lavendretta you do the same thing

[KyanasTube]

Thanks Mr.Pat!

[Gondriathecat]

Finally made sense of this nonsense.

[stealer111]

Do u teach at a school? if so where? cuz im movin there.

[amazzon44]

These are great videos. Thanks for taking the time to make them.

[atchisonj19]

7:24 you accidentally said negative 4 over negative 2 is negative 2, when your denominator was in fact positive 2. Just a minor thing, but great video nontheless! :D

[CatchFallingKnives]

Happy Now.

[kizhana]

Thankyou soo much Patrick... Great videos...:D :D :D helpin mee soo much..:) Thx :)

[hintless]

thank you so much for the video, helped alot keep making videos!

[faizcube007]

i think you should have placed a square bracket when you wrote the solution to the second rational inequality, because there was an equal choice as well... {3,+infinity)

[hintless]

@faizcube007 but 3 didnt satisfy the inequality becuase it was undefined

[ladiesman940]

THANX MAN I LOVE YOU

[AWPNubDiesel]

Dude, you're a boss. I'm doing a test review atm and had no clue how to do these types of problems, now I can, and have more notes. Thanks.

[patrickJMT]

@AWPNubDiesel come back whenever, i am always here!

[roxxyroll3r]

Ive watched like..20 of your vids now. You're amazing! Way better than my calc professor. My first exam is today. i really hope i can get an A!

[patrickJMT]

@roxxyroll3r i hope the test went well!

[mariakiss94]

@patrickJMT Thx!!!

:D

[lahirumc123]

you are a life saver Patrick, I don't know how to thank you enough. I was having such a tough time in Pre-cal I even thought of changing my major. Now thanks to your videos I have some hope. Thank you so much.

[patrickJMT]

@lahirumc123 my pleasure, spread the word to your friends ; )

[jocyrulesxoxo]

@lahirumc123 omg! i know how you feel. im a junior in high school with pre cal and i barely passed both of my algebra classes and they never gave me geometry. i ended up with analysis of functions so this was like the toughest thing to be in pre cal.

[spaceshot1332]

thx



[KrinkKut]

Thank you again man!

[lookingupsky]

thanks

[DORAshalala]

i understand everything except for the number line. how i want to know, i need to draw a solid circle or a circle on the number line? you just keep draw it as a circle and it seem that the number is not included.

[Gaspard1283]

Now i understand... you're ways more intelligible than my maths teacher!

[wbarkeley]

Be my teacher. Math actually makes sense.

[sophiegtv]

I. Love. You.

[phuckyutube615]

yea he fucked up its [3, infinite)

[Brutal252]

wait what would the last example be nothing makes it < then or = to 0 wtf

[maribates]

@Brutal252

He didn't explain, but the reason 3 is not included is specifically because it is not in the domain of the f(x), I don't know why he didn't point that out. Am I right?

[RossRocks07]

I was sick so I didn't go to school. My friend told that we learned radional inequalities. My first thought was Patrick would have a video on that...and you do. Thanks! :)

[zeshanshahzad]

how to solve rational inequality (x-3)/(x-2)<0 .... when i applied the given method the ans was wrong

[TheAdjundantReflex]

You should get paid for this...the American government, especially it's education policies, are becoming incredibly asinine. All good talent, like you, doesn't teach because of the ridiculous restrictions on teachers' unions and salary caps that are enforced in each state.

Ridiculous...anyways, thanks a lot for doing what you do.

[ChowRamen]

I have always wondered how you set up your camera.

[patrickJMT]

@ChowRamen duct tape and a stack of books

[EMOTIONZ80]

@patrickJMT DEDICATION >!!

[coolmafiaboy]

@patrickJMT lol , camera stand XDD

[01rai01]

@patrickJMT what kind of books??? just wondering

[haveen3]

you're amazing!! thank you!! for alll your videos! they immensely !

[nLoL2]

You explain this a lot more thoroughly than a conventional school teacher; are you in teaching?

[patrickJMT]

@nLoL2 i used to stand in front of a board and bore people, yes. not any more though.

[mbsimmer]

@patrickJMT so what do you do now?

[patrickJMT]

@mbsimmer stand on the corner and ask for change. sometimes i go to the public library to freshen up and make a video while i am there.

[Dewzy100]

@patrickJMT he's lying, he does stand up.....

[maniflora]

would answer to second example be x cannot equal to 0,-1 & the answer ( -1,0) U (0,1)U( 1,infinity)

[rockangel7777]

I suck at math ! where were you all my life ?

I totally needed help solving math problems ...

T H A N K Y O U ! like so freakin' much

[patrickJMT]

@rockangel7777 i have been here for about the past 2-3 years, i do not know about the rest of it!

[Moxin667]

Thanks, this was really helpful. Looking up your vids first if I'm lost in the future :)

[Zuleria92]

You're a god!~!!!

[karim7ahsan]

the difference between you and a teacher?

a typical math teacher has about 100 to 200 students in my school

while you have millions of US, the students! ;)

[patrickJMT]

@karim7ahsan glad i do not have to grade everything : )

[TheTrueSong]

I have one question: I was always taught when you had an equation that has a "Greater or Equal to" sign you shaded in the dot, but on your second example you left it open meaning "Stricter Than", you explain it as being "undefined" how did you figure that out? Thanks so much in advance!

[patrickJMT]

@TheTrueSong you can not divide by zero

[super1range]

thanks a lot.. i have a test this week i got few questions still tho

1. what if there are holes on the graph what do we do with that?

2. u know the signs of the inequalitly > < if we like multiply by negative or divide like it flips the sing of w/e i dont understand that, will it ever happen here?

[o32o32]

Thank you so much!

This helped a lot!

[TheyraCecilia]

Thank you soooo much! We are using ALEKS in my class and the program just solves it, and sometimes I can't figure out how the signs are figured out and when to use the Union sign and when not to! And this just made it much much easier! Thank you sooo much!

[LeeDwarf]

You are better that my teacher thank!

[goofguy316]

@dirt0jumping

couldn't agree more

you are an awesome teacher...learned more in 10mins than an hr of class

[patrickJMT]

@goofguy316 thanks. glad i was able to make some sense out of it for you

[abcchia]

legit your the best



[dirt0jumping]

I wish you were my High School teacher

[pillora003]

dude! thanks.! it helped me alot! i would thank u soo much after my exams man!! thanks!

[Troo44]

wow this guy better teacher than my Pre Cala college professor. Made that much more understandable. My teacher, always skips steps in her head, which throws me off time to time.

[TheCecile2010]

this was so helpful!

[wolfloverii]

wow thx a lot

[HerricksHigh]

I love you no homo

[50yer]

Thank God you made this video, your are the first person to explain that number line where it makes sense. Everyone else wants me to punch in the numbers and find the signs... very confusing. Thanks again.

[Sami132able]

patrickJMT, you're my neck saver. I've quesion: Can ou explain how can I solve this inequality on this format :0 ≤ c . n^2 ≤ a n^2 + bn + d ≤k 2 n^2,

for example c n^2 ≤ 1/2n^2 - 3n ≤ k 2^n2

for all n ≥ n0. where c, k are constanrts and greater than zero. Thanks a lot for your help.

[mundorff92]

This video helped me to understand it so much better.Thanks!!!!

[patrickJMT]

@mundorff92 no problem!

[Cyphlix]

can anyone tell me why you cant simplify the last fraction to just -1/x ?

-1(x+1)/x(x+1) should equal -1/x right? (eliminate (x+1) on numerator & denominator)?

[Skies678]

@Cyphlix The top is (-x+1) and it is equal to -1(x-1) and not -1(x+1)

Multiply each one to see for yourself. Hope this helps

[Cyphlix]

@Skies678 ahh k, thanks skies :)

[chelseafcfanisy]

I went from tears of pain to tears of happiness.

[patrickJMT]

@chelseafcfanisy ha, that sounds like a good direction to go : )

[stkeamza2]

my tears of frustration just dried up!

[smalltowndarlin]

thanks so much! (:

[Dookie4182]

hahahaha me and my friend kenny spent a good fourty minutes trying and failing miserably to figure out an inequality similar to the second one, only to be saved by youtube.

[diztorcion666]

thanks man .your an awesome teacher. i just needed some review and thanks to you i think i get now just need to gather the willpower to acually do the homework

[krissportygirl]

thank you so much, this is great!

but do you think you can show me how to solve this inequality:

2x^2 - x +5 / 3x^2 +x +7 is less than 2/3

[Yu2Kal]

@krissportygirl that question is pretty long if u want a solution i can scan mines in and send it to u via msn or something, since ur post was 2 months ago u might not want the answer anymore lemme know

[manutube8080]

excellent again.

[toobakhan1595]

thanksssssssssssssssss a lot !

[clau2gi2]

WoW, you are the best teacher I have ever had. Thank you, Thank you, Thank you, Thank you, Thank you ;)

[EuropaBloke]

GREAT video!

Very clearly explained, excellently executed, 5/5!!!

Thank you!

[krazycow1888]

you ARE AMAZING. i really appreciate your videos! they are soo helpful!!!

[pointnasty]

great video... saved my life.. thanks make more videos!

[hakux99]

You saved me a lot of headache by explaining that problem at around 5:30. Thank you so much.

I would have never thought to only plot one point if the numerator or denominator was missing a variable.

[FULLALCHEMIST1]

i lost?????????/????????????

[kellyanneland]

Great videos!

Can anyone help me with this problem;

(x + 1) / (x - 2) < 3

thanks

[warnford]

excellent, help from a most unexpected quarter !

[ffrisch2]

You are a good tutor man

[MrAkashGuha]

union is a data management term

[MrAkashGuha]

I didn't get the last question isn't -x + 1 = 0 should result in x = 1

[wolski888]

Is union or "u" used in the US? because I'm from Canada and we use just "OR"

[orlibloom4]

@wolski888 What part of Canada are you from? I'm from Manitoba and we use Union. So, not just a U.S thing.

[wolski888]

@orlibloom4 From Ontario, more specifically Guelph.

[wolski888]

Is this the algebraic way? or graphic since you use a number line..which is the x-axis.

[ownedncut]

maker of this video is one of the greatest human beings

thanks

[thechangee]

Great video!

[ladyiris313]

Ok, I just read my entire chapter and had NO idea what they were talking about, until I watched this. Grazie!

[Ronaldoo91]

mm sexy lol

[back2themusic]

Patrick is the best math tutor on youtube!

[jesusclau1]

Awesome! Thank you so much for your help!!

[sopranojenni]

very helpful video! thanks!

[rahmancbe]

Thanks a lot Patrick.. this is my comment n any websites.. but you really owe it.. thanks again..

[keetner]

I should just skip my math class, and watch these instead haha...kidding...

But I'm really glad you have these posted up! They're very helpful :D

Thanks!

[ineverfakejumps]

I have a question. At 8:03, why can't you just cross-multiply? I know you said it's because you have to have zero on one side, but why do you have to? It's because you may miss out one solution if you cross-multiply, right? But why exactly would you miss out a solution? Sorry, I guess I understand all this in theory but don't actually know why.

[ineverfakejumps]

Oh, never mind, I think I just understood it.

[Ronaldoo91]

because u gotta set it equal to zero, cuz when u start plugin in numbers, u gotta know if its greater or smaller than 0

[blackdranfire]

For the common denominator thing I thought you have to multiply the same thing on both sides of the equation

[CygnusWing20]

THANK YOU THANK YOU THANK YOU!!!!

[tysonjones87]

Amazing... thank you

[sandk10]

Thank you so much, my teacher does not explain anything well and today i just kind of came across your videos. they are a lifesaver

[TragicTofu]

Hi PatrickJMT! You are so helpful! I am pretty sure I understand your method. But when I type the inequalitity into a calculator the answer is different! PS do you never have an greater/less than and equal sign because the denominator is always 0?

[username14657]

Marry me. I will have your babies and cook delicious meals for you, and we will lead a happy life surrounded by our 25 children who shall all be math prodigies thanks to you!!!

[patrickJMT]

the most flattering comment ever!

however, once you mentioned babies, you lost me. typical guy, i guess.

still, very nice of you. : ) a lovingly cooked meal is always most appreciated.

[username14657]

Okay, we'll use birth control!

And just wait till you taste my cooking :D

[patrickJMT]

mmmm i love good food!

i am right handy in the kitchen myself : )

we can have an iron chef cook off - then we just eat it all!

[XxlilGelixX]

@username14657 lmfao :DDD



[Gewgala]

Thanks a million times over. Left handed people rock!

[16kn]

My Hero ^_^

[ana469]

thanks so much!!

[bodenbadger]

Thank you thank you thank you!!!!!!

[bansh8]

Holy crap man you help so much. I'm going over your different videos for my math final tomorrow.

[Jaquis198]

thank you very much. i've got a quiz on this tommorow for my algebra 2 honors class and my teacher went over this in like 4 minutes before the bell rang. you helped me out a lot. thank you very much!

[fzvibe]

Actually nvm... the denominator can't be 0. I will take back my last comment.

[fzvibe]

The second example's interval should be [3, infinity) remember, you only use small bracket when x cannot equals to 3.

[jbrambleuno]

Way better at this than my prof.

[gamesm]

thank u

ur explanation is really great

[siddharthshah]

Thanks a lot man Aesome tutorial helped me a lot

[patrickJMT]

glad i could help!

[moniic13]

thank you so much:)

ur way better than my professor:)

[patrickJMT]

aww yea! : )

[patrickJMT]

thanks! : )

[Bumbles5]

Thank you so much! This helped me beyond belief, we were on the brink of getting a tutor, and well we cant afford one really but I found your vid and it saved my family a lot of stress and me from a failing grade. Merci!

[patrickJMT]

my pleasure! glad to help! this is the same stuff i show people that i tutor, only i charge a lot of money to show it! : ) of course, the only problem is that you can not get any answers from a video when you ask them!

good luck!

[tvuong88]

Hi patrickJMT, If I have question would like your help, Ho can I contact you? Perhaps, Can you give me your e mail addressed. Thanks and please let me know soon.

[patrickJMT]

well, you can always post questions on videos or through my youtube account. be warned though that i get about 100+ questions a day and after working 12 hour days myself, i usually do not get around to answering many of them!

[tvuong88]

Can you show me how to post questions on videos or through my youtube account , because I do not know how to do it and Sometime If I have math question and would like to discuss to you personaly, Not for public. So, I think it would be great if I have your e mail address so thAT We can discuss question privately.

[tvuong88]

Great! Thank You patrickJMT .

[patrickJMT]

no problem!

[jaathan]

Thank you so much!! My teacher was tryin to teach this and man were we lost. Your video was clear, detailed, and straight forward. Thanks again. By the way did I mention you have reali neat writing?

[patrickJMT]

glad it helped! my hand writing is normally that of a first grader, but i try to keep it clear in the videos!

[Salavat23]

You are amazing, a life saver!

[jon4012]

Simply awesome! I missed out on this one day and my test is tomorrow, you are a life saver!

[ekim88983500]

you always have to be careful with inequalities... and i know there are several methods for doing it... graphical method, or the critical region method, and my teacher's always telling me to be careful about dividing by negative numbers cos u have to switch the sign around.. but this is deffinately the best method i've seen (the number line mehtod).. I be using this method from now on.. great stuff as always.. keep 'em coming!