Basic Inequality

[vivid forum]

ok so I'm new to math and have no clue how to solve this inequality. I have been taught to solve this with wavy curve method. I have factorised the numerator into (x-2) and (x-4) but don't know what to do about the denominator. Thank you in advance

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[vivid forum]

need help kinda urgently guys

[icy spear]

Hi

[vivid forum]

hello

can you help me, please?

[icy spear]

Hey

Solve the denominator too

X ≠ 3

Yo , here the thing is that the denominator will always be positive , do you agree?

@vivid forum

[vivid forum]

huh?

how

It can be positive or negative right, since root of something is +/-

I'm new to math so tell me if I'm wrong

[icy spear]

Suppose y = x^2

[vivid forum]

👍

[icy spear]

x can be [ +sqrt(y) ] and [ - sqrt(y) ]

[vivid forum]

yeah

[icy spear]

Here the Sqrt( 3 - x ) has a "plus" sign in front it

[vivid forum]

wait, it works like that?

[icy spear]

Ok Consider

Y^2 = ( 3 - X )

So you will get

So Y = ±sqrt( 3 - x )

[vivid forum]

yeah

[icy spear]

Also notice one thing here

The condition given here in the question is the "Expression is less than or equal to 0"

[vivid forum]

Yeah

[icy spear]

So you told that you factorised the Numerator right?

You did wavy curve method?

[vivid forum]

yes but I am unable to apply it with root in denominator

[icy spear]

In Sqrt( 3 - x ) , 3 - x should be positive

[icy spear]

For it to be defined

So 3 - x > 0

By the denominator ≠ 0 also

So 3 - x > 0

x - 3 < 0

x < 3

I will send you a photo of wavy curve method

Of the whole thing

[vivid forum]

I think I'm getting it

[icy spear]

Mmm, can you do it?

[vivid forum]

Yeah let me try

[vivid forum]

Wait so should I just get rid of the denominator in the original inequality and then take intersection of both

[icy spear]

You should take the region where x^2 -6x + 8 is negative

Can you send me a photo of how you are doing?

[vivid forum]

oh

I took it as positive

Nvm I got the sign wrong

[icy spear]

It should be negative , so the whole thing will be less than or equal to 0 according too the question

[vivid forum]

I'm getting (3,4]

Which is an option

[icy spear]

What are the options given

Can you specify?

[vivid forum]

Ok wait nvm

I got the answer

[vivid forum]

[2,4], [2,3), (3,4], [2,4] - {3}

I think it is [2,3)

If I am not wrong

[icy spear]

Is it there as any option?

[vivid forum]

yes, these are the options

[icy spear]

Yes

It's right

[vivid forum]

thanks for your help 👍

[grizzled star]

@vivid forum has given 1 rep to @icy spear

[vivid forum]

@icy spear can I add you. If you don't mind.

I mean I might need help again if you are good with that

[icy spear]

Yes I am always ready dude

Anytime 😊

[icy spear]

👍

Send me the request then

[vivid forum]

Thanks again👍

[grizzled star]

@vivid forum has given 1 rep to @icy spear

[icy spear]

Ya np

[vivid forum]

Do I just leave this post now

[icy spear]

Yeah

Close it

+close

I think you should do it

[vivid forum]

+close