Solving a Parametric Inequality

[@hsjkdsgd]

I don't turn on notifications for any channel but I'm forced to turn it on for this one

[@SyberMath]

Well, thanks!!!

[@leecherlarry]

very nice one! compi finds four cases, thanks! *Reduce[a x/(x - 1) > 1, x] // TraditionalForm*

[@זאבגלברד]

It is nice to know that the left side is a y=k/x function that was mooved. Its asymptotus are y=a , x=1 So it is very easy to draw it for every case of a. And now we have the line y=1 that intersects this function. This way we can unswer graphically. In the general case y=(ax+b) / (cx+d) is such a y=k/x function. [It can also be a straight line]. Simply devide polinom by polinom to see the movement.

[@SyberMath]

I love your approach!

[@tonyhaddad1394]

I like how you get every time a new kind of problem !!!!😍

[@SyberMath]

Haha, thanks!

[@salomenaskidashvili8230]

Thank you for this awesome video. Can you do a video on some easier parametric inequalities too? There is so little resurces on this topic, maybe you can share some if you know them too. Thanks in advance.

[@SyberMath]

Great suggestion! I can come up with easier ones and share. Here is one off the top of my head: (a-1)x

[@AlexandreRibeiroXRV7]

Hey, Syber, love your content! If I may ask, is there a way to submit video ideas for you?

[@SyberMath]

Good question! I think I will copy Michael Penn and make a form for submitting video ideas? 😁😁😁

[@bigjazbo9217]

Wonderful exposition! In your final solution set, the third and fifth lines can be combined if you change the third line to be 1

[@SyberMath]

Thank you!!! That's correct. I guess I just wanted to write them separately because those are special values.

[@leif1075]

@@SyberMath Don't you think it's ok and smart to multiply both sides by x minus 1..it's the first thing Indid..and dont you think it's what most people would do?

[@leif1075]

@@SyberMath wait you contrsdicted yourself at 2:44 x cannot equal 1 then thst RHS would equal infinty because you have zero in the denominator!? At 2:18 you even say x can't equal 1...

[@SyberMath]

@@leif1075 I don't think so. For example, if you were solving x/-4

[@SyberMath]

x=1 is not a solution of the inequality. It's a root in the sense that the sign of the expression changes at x=1. That's what we base the table on.

[@joaquingutierrez3072]

Thank you for the video :). Nice problem

[@SyberMath]

Glad it helped

[@CriticSimon]

This is so challenging!

[@SyberMath]

Yes it is! But it's fun at the same time, isn't it?

[@CriticSimon]

@@SyberMath Yes it's fun

[@tonyhaddad1394]

12:56 how can we know if (a-1).X+1 Is always negative , when a is between 0 and 1 the coefficient of x is always negative okay but when we plus 1 the absolute value of [(a-1).x)] must be bigger than 1 to get a negative numerator ??? !!!!

[@SyberMath]

When a

[@tonyhaddad1394]

@@SyberMath thanks for clarifiying 💓💓

[@SyberMath]

No problem 🥰

[@Magistrixification]

15:26 Why is x

[@SyberMath]

Because that's what the table gives us for that interval of a.

[@yoavmor9002]

@@SyberMath Nope, hate to be that guy but I'm pretty sure it's just a simple copying mistake... Nowhere anywhere is there a 1/a. I absolutely hate those kinds of mistakes, they ruin my grades to no end

[@barakathaider6333]

👍

[@michaelempeigne3519]

I would square it at beginning

[@SyberMath]

Good thinking

[@adamelbouazzaoui4166]

a/(1_a) is less than a

[@robertcotton8481]

"X-1" can't be zero else it unsolvable from start

[@SyberMath]

That's right!

[@michaelempeigne3519]

a^2*x^2 > x^2 -2x+1 (a^2-1)*x^2 +2x -1 > 0 Solve this inequality

[@SyberMath]

How do you solve that inequality?

[@michaelempeigne3519]

Note: if you find the roots of that : it yields x = [ abs ( a ) - 1 ] / ( a^2 - 1 ) and also x = [ - abs ( a ) - 1 ] / ( a^2 - 1 )

[@michaelempeigne3519]

Neat method for finding lcm and gcf of two numbers.

[@SyberMath]

Nice

[@krishnannarayanan5252]

U r very very slow in English. It should be faster atleast 5 times faster and more use of so, cool OK etc more so that laymen like us will learn maths well

[@mohammadsaddam3736]

Didn't understand 👎

[@SyberMath]

This is a deep topic! You will eventually get it! Replace a with numbers from that interval to see how that works!