I've always messed up problems associated with inequalities and absolute values. You're a life saver Philip! Can't believe I'm bossing every single one of these questions now!! Hands down THE BEST EXPLANATION available anywhere.
It ain't phantasmagorical to promulgate that "YOU ARE THE MOST FINESSE TUTOR ONLINE FOR GRE". Your videos are repleted with cognizance and its jovial to watch.
Ow wow, I gained a lot from your vocabulary. I hope your words all show up on my test. But for sure Philip's synoptic GRE insights, tips and material are by far the best you can find online...… And trust me I have perused quite a number of different tutors out there. GREAT job Philip. Keep them coming.
I'v been doing the Magoosh study plan that I paid for to study for the GRE, but in my opinion these videos are way more helpful and explain things in such an accessible way! Thank you!
I've gone through Magoosh, Princeton and their online materials. Nothing is even remotely close to every single topic that you cover and the tips that you provide, hats off to the wonderful work.
I can see my growth as an individual and that's the greatest gift one can ever get! Gratitude Philip and Thank You So Much Once Again...We need more Human like you, who can explain math's the way that even a child can learn!🥺💯
I gained a lot from this inequality video. Different techniques for different questions. Had you not been here, this wouldn't have been possible. Thank you so much Philip.
the question at 16:46, set A get rid of the absolute values and subtract y from Both sides of the inequality, then you have x-y>0 since setB is x+y>0 this shows that Xis absolutely bigger than Y
Most comrehensive explaination on absolute values and inequalities EVER !!! I used to get baffled everytime, but now I won't be so ! Thank you so much you are the best !!!
I'm prepping for the GRE General Test. When I saw an absolute value inequality I didn't even know what it was. Thank you for focusing on the philosophical aspect. It made this so much easier and simpler to understand. THank you very much!
🎯 Key Takeaways for quick navigation: 00:00 🎬 The video covers absolute values and their applications in GRE / GMAT Quant. 01:09 🧠 The output of an absolute value is always positive, regardless of the input's sign. 02:14 📚 Understanding the core essence of absolute values is crucial for solving complex problems. 03:34 🔍 Analyzing absolute value inequalities requires considering both positive and negative input scenarios. 05:44 🤔 A negative number inside an absolute value can result in a larger positive output due to the sign removal. 08:12 🤖 Absolute value questions often involve reasoning about scenarios where variables could be positive or negative. 10:42 ⚖️ Comparing quantities involving absolute values requires considering multiple possibilities, including variables being zero. 12:30 🧮 Solving equations with absolute values involves considering both positive and negative input values. 14:55 🔀 Inequalities with absolute values require solving two separate scenarios, one with a plus outside the brackets and one with a minus. 17:23 📐 Absolute value equations and inequalities often necessitate solving multiple scenarios to account for different input sign possibilities. 22:18 📈 Applying the concept of absolute values in solving inequalities involves analyzing both positive and negative input cases. 25:00 🤯 Handling integer solutions in absolute value inequalities requires considering all possible scenarios for the variable's sign. 25:41 🔍 Solving equations with a variable inside and outside an absolute value requires calculating two scenarios. 26:20 🔄 When a variable equals another variable in an absolute value equation, solving both scenarios is necessary. 26:48 🔀 Replace the absolute value with both positive and negative scenarios, then solve for each variable. 27:28 🧐 Check the solutions by substituting them back into the equation; one of the solutions will be valid. 28:11 🎯 A variable in an absolute value equating a variable outside it often requires solution validation for correctness. 28:51 ❗️ Checking solutions for validity is particularly useful when a variable inside the absolute value equals another variable outside it. Made with HARPA AI
Philip, I don't know how I would manage to learn so many concepts without you. Tried so many sources but I was unable to get absolute value but this video has helped me grasp it at once. You are doing so amazing. Please make some fresh videos on reading comprehension.
Thank you, Philip! You are a lifesaver, I have understood all of the concepts, and your practice problems have helped me test those concepts as well you are a fantastic tutor.
Decent video. Here's bunch of examples I've encountered in different places (my highschool, forums, textbooks, other videos) that might be helpful. I'll skip the definition and list some properties. The proofs can done by cases or some tricks using previously proved properties, they are available online. a) |ab|=|a||b| b) |a|=b b>=0 and (a=-b or a=b) c) |x| < a -a < x < a (when a is negative also works) d) |x| > a x>a or x =0 and (a=-b or a=b) (check that 2x+2 is above 0) or by cases x>=1 and x-1=2x+2 => x =-3 but contradiction with previous assumption x x = -1/3 fine note squaring (x-1)^2=(2x+2)^2 only works when we assume 2x+2 >= 0 2. |x-1| -1/3 and x > -3 x > -1/3 3. |x-1| -3 or x < -1/3 (all x) and -|2x+2| < x-1 |2x+2| > -x+1 2x+2 > -x+1 or 2x+2 < x-1 x > -1/3 or x < -3 so x > -1/3 or x < -3 4. |x| + |x-1| = 2 (when sum of distances from 0 and 1 is equal to 2) cases x >=1 2x-1=2, x = 3/2 ok 00 => because x+y>0, then x-y>0 x>y 7. Graph |x|+|y|=1 By cases or properties or squaring |y|=1-|x| or x+y=1 and noticing it's symmetrical to the lines x=0 and y=0 8. ||x|-|y||0 what's the other side? Pythagorean theorem 4a + x^2 = a^2+2a+1 x = sqrt((a-1)^2) = |a-1| 12. If there are two lines m:2x+y+1=0 and n:x-2y+3=0, what are the bisector lines(divide angles of lines crossover by two)? Points (x,y) on bisector lines are such that their distance is equal from lines m and n so (distance formula |Ax+By+C|/sqrt(A^2+B^2)) |2x+y+1|/sqrt(5)=|x-2y+3|/sqrt(5) |2x+y+1|=|x-2y+3| Now either solve by cases, or recall |a|=|b| a=b or a=-b, or square |a|=|b| a^2=b^2 a^2-b^2=0 (a-b)(a+b)=0 (2x+y+1-x+2y-3)(2x+y+1+x-2y+3)=0 13. When the line going through point (2,0) is perpendicular to circle x^2+y^2=2 Line a(x-2)=y ax-y-2a=0 Now either x^2+y^2=2 and ax-y-2a=0 equations have to have one solution or distance from line to point (0, 0) is equal to circle radius. |a * 0 - 1 * 0 -2a|/sqrt(a^2+1)=sqrt(2) |-2a|=sqrt(2)*sqrt(a^2+1) 4a^2=2a^2+2 a^2=1 a=+-1
Now I will use this two solutions approach I know it may be easy to the majority of people but I remember how in school I either missed it or didn't understand this concept and only occasionally saw other using it. Now in my 20s I finaly encountered with it again and understood it! Thank you a lot! I must do practice questions on this
Last question was a surprise for me. I never checked the validity of the solutions for variable = variable in absolute type of question. Thanks a lot for making this video.
I loved your video. Absolute values are more "valuable" than we realize (pun intended). They are essential to the algebraic formula for a square, which you never see in math courses. |(x+y)+(x-y)| = r is the formula for a square centered on (0,0) with sides of length r. On more thing. The reason -1 doesn't work in your final equation, |x| = 4x+3, is that an absolute number can NEVER be negative!
You are a great teacher, for some reason I have always made mistakes in absolute value questions and you have made most of my doubts go away. I will keep your advice in mind for my exam "stay calm". Thanks
Somehow I ended up watching one of your video and I am watching all videos !! Thanks to UA-cam for suggesting your video at a very crucial time. You really need a big shoutout. Kindly keep up good work!
I for the life of me could not figure it out, did pre med and studied business and legit could nt understand what the f was going on. Thank you so much man means alot!
thank you SOOOO SO much for explaining that last point!!! i could not figure out why i kept getting the wrong answers when i thought my methods and formulas were all right i literally thought i was going crazy. i cant believe no gre test prep book ive come across has explained that and in literally 2 mins you just cleared up all the confusion in my head. you're the best :)
Thank you so much sir! This video was really helpful. You are a legend and your explanation is fabulous. This channel is so underrated and I really wonder how come you have so less subscribers? Keep growing and may god bless you!
so the answer to the practice Q where x>y given will be option D right? as they cannot be determined, since the answer comes different every time, whether we choose y as a positive, negative or 0
Your videos on quants are really helpful to people like me who are really afraid of this section. Ever since I got a hold of your videos a couple of weeks ago, my level of confidence has really increased and I am able to solve even difficult questions. Thank you so much Phillip! Your videos really have to reach people who are in search of good GRE/GMAT content and I will try my best to help you with that. Thanks again and have a great day!
Such a fantastic teacher you are! You explain so well and I only wish I had found your videos sooner! I am on your 4th video and can’t wait to get to the others as I have a less than 3 weeks for the exam! Also I love the way you explain things so clearly yet calmly! Keep up the brilliant work you do!
Hey Philip! I love your videos and they're a life saver! I just had one doubt, in the question at 16:54 minutes, couldn't y be zero? In which case the answer would be D right?
Great video yet again! This is the best thing about your videos, you know exactly where would the students be struggling and you give the most logical explanations to them and they no longer seem so difficult.. thank you 👌
Hey, absolutely brilliant video. Just a request though, could you please share the answers to all the questions in the description or comments, please?
Your videos are helping me a lot to boost my quants as well as verbal knowledge. I have scheduled my GRE exam for next month. Looking forward to get more videos on some last minute tricks for exams
![Quartiles, Percentiles, Quintiles, Interquartile Range, Box Plots [worked examples! Oh wow]](/img/n.gif)
I've always messed up problems associated with inequalities and absolute values. You're a life saver Philip! Can't believe I'm bossing every single one of these questions now!!
Hands down THE BEST EXPLANATION available anywhere.
Thanks for this shobbada!!
Literally a life saver! I am sooo so grateful !
"If you stay calm, life will be much easier." - Phillip, the tested tutor, 2020.
I'll always keep it in mind Sir.
Perfect! :)
It ain't phantasmagorical to promulgate that "YOU ARE THE MOST FINESSE TUTOR ONLINE FOR GRE". Your videos are repleted with cognizance and its jovial to watch.
Amazing comment! Extraordinary vocabulary!
@DAVID KUUSAAL TINGAN Thanks a lot!. Good luck to you too.
Ow wow, I gained a lot from your vocabulary. I hope your words all show up on my test. But for sure Philip's synoptic GRE insights, tips and material are by far the best you can find online...… And trust me I have perused quite a number of different tutors out there. GREAT job Philip. Keep them coming.
I'v been doing the Magoosh study plan that I paid for to study for the GRE, but in my opinion these videos are way more helpful and explain things in such an accessible way! Thank you!
Great to hear Sarah!
I've gone through Magoosh, Princeton and their online materials. Nothing is even remotely close to every single topic that you cover and the tips that you provide, hats off to the wonderful work.
Wow, thanks Aravind
@@TheTestedTutor I know you've done a video on AWA, but could you show us a live example of tackling say an issue task and an argument task
Your lessons are worth paying for. But for people like me such free classes are a blessing. Thank you.
Thanks so much Arghya
I can see my growth as an individual and that's the greatest gift one can ever get!
Gratitude Philip and Thank You So Much Once Again...We need more Human like you, who can explain math's the way that even a child can learn!🥺💯
I can't believe this content is free!
best test prep channel ever. thank you so much for this.
Whether this video gives me a negative or a positive result on test day, I must say I absolute-ly loved it ;)
Thanks again Philip, you are truly "The Trifecta." If you feed them, they will come. I came back to another fruitful video...keep them coming!
I gained a lot from this inequality video. Different techniques for different questions. Had you not been here, this wouldn't have been possible. Thank you so much Philip.
Thanks so much Hassan. Really glad it has helped. You have been there from early on.
from this video, I only learned this: "Always check the answers when VARIABLE=VARIABLE in ABSOLUTES", which is gold advice. Thanks Philip!
This man out there saving lives. You da real MVP.
Thanks VR!
phillip you are the best ........... period
the question at 16:46, set A get rid of the absolute values and subtract y from Both sides of the inequality, then you have x-y>0 since setB is x+y>0 this shows that Xis absolutely bigger than Y
Most comrehensive explaination on absolute values and inequalities EVER !!! I used to get baffled everytime, but now I won't be so ! Thank you so much you are the best !!!
I'm prepping for the GRE General Test. When I saw an absolute value inequality I didn't even know what it was. Thank you for focusing on the philosophical aspect. It made this so much easier and simpler to understand. THank you very much!
the greatest teacher of GRE.
Haha thanks Ayesha :)
🎯 Key Takeaways for quick navigation:
00:00 🎬 The video covers absolute values and their applications in GRE / GMAT Quant.
01:09 🧠 The output of an absolute value is always positive, regardless of the input's sign.
02:14 📚 Understanding the core essence of absolute values is crucial for solving complex problems.
03:34 🔍 Analyzing absolute value inequalities requires considering both positive and negative input scenarios.
05:44 🤔 A negative number inside an absolute value can result in a larger positive output due to the sign removal.
08:12 🤖 Absolute value questions often involve reasoning about scenarios where variables could be positive or negative.
10:42 ⚖️ Comparing quantities involving absolute values requires considering multiple possibilities, including variables being zero.
12:30 🧮 Solving equations with absolute values involves considering both positive and negative input values.
14:55 🔀 Inequalities with absolute values require solving two separate scenarios, one with a plus outside the brackets and one with a minus.
17:23 📐 Absolute value equations and inequalities often necessitate solving multiple scenarios to account for different input sign possibilities.
22:18 📈 Applying the concept of absolute values in solving inequalities involves analyzing both positive and negative input cases.
25:00 🤯 Handling integer solutions in absolute value inequalities requires considering all possible scenarios for the variable's sign.
25:41 🔍 Solving equations with a variable inside and outside an absolute value requires calculating two scenarios.
26:20 🔄 When a variable equals another variable in an absolute value equation, solving both scenarios is necessary.
26:48 🔀 Replace the absolute value with both positive and negative scenarios, then solve for each variable.
27:28 🧐 Check the solutions by substituting them back into the equation; one of the solutions will be valid.
28:11 🎯 A variable in an absolute value equating a variable outside it often requires solution validation for correctness.
28:51 ❗️ Checking solutions for validity is particularly useful when a variable inside the absolute value equals another variable outside it.
Made with HARPA AI
These videos are definitely worth making Sir ✨✨✨✨✨
God bless you
Best explaination for absolute values ques.
As I am progressing towards my GRE exam date, your videos are proving to be a great savior! Thank you Philip!
Happy to help Yatri!
this dude is the GOAT! thanks so much for the help
Honestly, will never be able to fully express my gratitude to you for these amazing videos you post! Thank you so much!
Thank you for that wonderful comment Shruti
Philip, I don't know how I would manage to learn so many concepts without you. Tried so many sources but I was unable to get absolute value but this video has helped me grasp it at once. You are doing so amazing. Please make some fresh videos on reading comprehension.
Hahathank you. I will
Thank you, Philip! You are a lifesaver, I have understood all of the concepts, and your practice problems have helped me test those concepts as well
you are a fantastic tutor.
this is probably the best video on this topic. love ur energy man. u are a saver.
Decent video. Here's bunch of examples I've encountered in different places (my highschool, forums, textbooks, other videos) that might be helpful.
I'll skip the definition and list some properties. The proofs can done by cases or some tricks using previously proved properties, they are available online.
a) |ab|=|a||b|
b) |a|=b b>=0 and (a=-b or a=b)
c) |x| < a -a < x < a (when a is negative also works)
d) |x| > a x>a or x =0 and (a=-b or a=b) (check that 2x+2 is above 0)
or by cases
x>=1 and x-1=2x+2 => x =-3 but contradiction with previous assumption
x x = -1/3 fine
note squaring (x-1)^2=(2x+2)^2 only works when we assume 2x+2 >= 0
2. |x-1| -1/3 and x > -3
x > -1/3
3. |x-1| -3 or x < -1/3 (all x)
and
-|2x+2| < x-1 |2x+2| > -x+1
2x+2 > -x+1 or 2x+2 < x-1
x > -1/3 or x < -3
so x > -1/3 or x < -3
4. |x| + |x-1| = 2 (when sum of distances from 0 and 1 is equal to 2)
cases
x >=1 2x-1=2, x = 3/2 ok
00 => because x+y>0, then x-y>0 x>y
7. Graph |x|+|y|=1
By cases or properties or squaring |y|=1-|x| or x+y=1 and noticing it's symmetrical to the lines x=0 and y=0
8.
||x|-|y||0 what's the other side? Pythagorean theorem
4a + x^2 = a^2+2a+1
x = sqrt((a-1)^2) = |a-1|
12. If there are two lines m:2x+y+1=0 and n:x-2y+3=0, what are the bisector lines(divide angles of lines crossover by two)?
Points (x,y) on bisector lines are such that their distance is equal from lines m and n so (distance formula |Ax+By+C|/sqrt(A^2+B^2))
|2x+y+1|/sqrt(5)=|x-2y+3|/sqrt(5)
|2x+y+1|=|x-2y+3|
Now either solve by cases, or recall |a|=|b| a=b or a=-b, or square |a|=|b| a^2=b^2 a^2-b^2=0 (a-b)(a+b)=0 (2x+y+1-x+2y-3)(2x+y+1+x-2y+3)=0
13. When the line going through point (2,0) is perpendicular to circle x^2+y^2=2
Line a(x-2)=y ax-y-2a=0
Now either x^2+y^2=2 and ax-y-2a=0 equations have to have one solution or distance from line to point (0, 0) is equal to circle radius.
|a * 0 - 1 * 0 -2a|/sqrt(a^2+1)=sqrt(2)
|-2a|=sqrt(2)*sqrt(a^2+1)
4a^2=2a^2+2
a^2=1
a=+-1
Wow most detailed comment I have ever read. Super extensive examples and commentary, thank you so much PN!!
Math is just like grammar. Just when I think I know it all, there appears an exception! Thanks, Philip, for clearing things up for us!
Your videos made a lot of problems easier for me!
Glad to hear that sanika!
your content is preternatural tested tutor! kind regards from Florida!
quite helpful, almost gave up studying on absolute value for my GMAT thanks a bunch though you're a lifesaver
I am in love with your videos😍😍 Math now seems interesting ❤️❤️
Thank you so much Kabita
These videos are worth making 🙏🏻.
another banger, came out knowing much more than i did coming in :)
Simple, direct and easy to reason explanations, there is great value in this video.
Thanks Natalia
You made the concept so easier Philip! Kudos
Learn to love mathematics again with Philip!
If I do well in the quant section of GRE, it’ll be only because of your videos. I haven’t done maths in over 12 years! Love your work and effort :)
That's lovely Shibani. Keep going!
Now I will use this two solutions approach
I know it may be easy to the majority of people but I remember how in school I either missed it or didn't understand this concept and only occasionally saw other using it. Now in my 20s I finaly encountered with it again and understood it! Thank you a lot! I must do practice questions on this
Last question was a surprise for me. I never checked the validity of the solutions for variable = variable in absolute type of question. Thanks a lot for making this video.
I loved your video. Absolute values are more "valuable" than we realize (pun intended). They are essential to the algebraic formula for a square, which you never see in math courses. |(x+y)+(x-y)| = r is the formula for a square centered on (0,0) with sides of length r.
On more thing. The reason -1 doesn't work in your final equation, |x| = 4x+3, is that an absolute number can NEVER be negative!
Thanks for this video. I have understood where I had not understood.
The last question of variable=variable really saved time.. Thanks Phillips
I always got confused with inequalities and abs values,but now I can understand concepts. Wish I could give multiple likes
Thank you so much for these well explained topic wise videos, I was able to score well in gre because of these
You made it super easy to understand even the complex questions..!!!
This videos are worth making, sir, love'em
You are a great teacher, for some reason I have always made mistakes in absolute value questions and you have made most of my doubts go away. I will keep your advice in mind for my exam "stay calm". Thanks
This is priceless! Thank you so much Philip!!!
This video really helped me understanding absolute value which was giving me much trouble lately.
Thanks from Bangladesh 🇧🇩🇧🇩
You are most welcome Tarannum
Somehow I ended up watching one of your video and I am watching all videos !! Thanks to UA-cam for suggesting your video at a very crucial time. You really need a big shoutout. Kindly keep up good work!
Thank you Philip! you are the best!!
Thanks Amanda!
I for the life of me could not figure it out, did pre med and studied business and legit could nt understand what the f was going on. Thank you so much man means alot!
I needed this thanks to your relentless help you keep giving us till this we appreciate it
thank you SOOOO SO much for explaining that last point!!! i could not figure out why i kept getting the wrong answers when i thought my methods and formulas were all right i literally thought i was going crazy. i cant believe no gre test prep book ive come across has explained that and in literally 2 mins you just cleared up all the confusion in my head. you're the best :)
You are so welcome Lily!
I really appreciate the way ur working hard for gre aspirants..ur videos helped me alot in improving my vocab... please dont stop making videos
I won't, inshallah.
This video is great. I always struggled with absolute values and inequalities. Please keep uploading tutorials. It really helps.
More to come!
Philip The LIFESAVER! Thank you soo much for making such informative videos. Keep'em coming!
We owe you a lot brother 🙌
More to come!
Thank you so much sir! This video was really helpful. You are a legend and your explanation is fabulous. This channel is so underrated and I really wonder how come you have so less subscribers? Keep growing and may god bless you!
All of your videos are so high value. Thank you so much!
so the answer to the practice Q where x>y given will be option D right? as they cannot be determined, since the answer comes different every time, whether we choose y as a positive, negative or 0
An absolute gem! ;D
I'm clear with absolute values. Thanks a ton.
Thank you for this video. I had little knowledge on this topic before and now I am more confident.
Wonderful!
very helpful videos, thank you for teaching us
Your videos on quants are really helpful to people like me who are really afraid of this section. Ever since I got a hold of your videos a couple of weeks ago, my level of confidence has really increased and I am able to solve even difficult questions. Thank you so much Phillip!
Your videos really have to reach people who are in search of good GRE/GMAT content and I will try my best to help you with that.
Thanks again and have a great day!
Wow thank you so much Suella. So glad your confidence is higher!
Best resource for GMAT
Loved the way you taught. Especially the 'pace' .
keep up the good work
Best videos ever!
Hey! Great Video. I Have my GRE on 28th September. Your videos really help understand the different scenarios. Very Useful. Great Work!!
Such a fantastic teacher you are! You explain so well and I only wish I had found your videos sooner! I am on your 4th video and can’t wait to get to the others as I have a less than 3 weeks for the exam! Also I love the way you explain things so clearly yet calmly! Keep up the brilliant work you do!
Cheers to learning!!! Great work Sir, thanks for making learning interesting.
Ineffable video!! It just solved all the doubts and struggles I was going through while tackling such questions..Thanks a lot Philip!!
Awesome video, with lots of examples!! Thank you so much Philip!!
Your videos are always so thorough!
I try Amina
You deserve more likes
Thanks MJ
Thank you so much for this video, I really appreciate all the hardwork that went into it
Thanks a lot! I've greatly benefitted from your video series. Really grateful!
I really really appreciate your great work Philip.you are such a wonderful and talented teacher
Thank you so much Hansi
I think I know the thing, however, watching the video I just figure out how hasty I do the test. I realy appreciate your videos man. 🤝
Brilliant lesson! Thanks Phillip
Thank you so much for making our lives easier with your hard work. Really enjoy learning from you. learning has never been this fun.
Your videos helped me a lot. God bless you
Inequalities made easy!! Brilliant
Thankyou so much fro making these videos for us! I feel so much more confident now! Love your content
I'm so glad!
Hey Philip! I love your videos and they're a life saver! I just had one doubt, in the question at 16:54 minutes, couldn't y be zero? In which case the answer would be D right?
Thanks Krittika! Even if y were zero x would still have to be positive to make x + y > 0. So x is still greater.
@@TheTestedTutor right. Thanks for such a prompt response!
Great strategy! Highly appreciate your efforts!
Great video yet again! This is the best thing about your videos, you know exactly where would the students be struggling and you give the most logical explanations to them and they no longer seem so difficult.. thank you 👌
Thanks Mansi! I used one of your questions!
@@TheTestedTutor yes! Was able to solve the rest of the questions I had sent u easily after this video..
@@mansib2228 That's great news !
The best videos!!!!!
last lesson is simply hilarious!!!!!!
Love watching your videos Philip, big fan.
Thanks so much Hassaan
Great video as always! Keep up.
Thanks Alpha!
Awesome concepts, you are helping in getting the basics right. Cheers!
I always struggled with absolute values questions. This video helped me clear the clutter and to have a better understanding about the concept .
Hey, absolutely brilliant video. Just a request though, could you please share the answers to all the questions in the description or comments, please?
Brilliant stuff
Thank you, Philip!
Your videos are helping me a lot to boost my quants as well as verbal knowledge. I have scheduled my GRE exam for next month. Looking forward to get more videos on some last minute tricks for exams
All the best
Your score?