Calculus

Calculus

Postby Guest » Tue Apr 10, 2018 9:53 am

I just do not know how to solve an inequation with variables in two fractions on both sides of the inequation. I apologize for my english, I'm from Brazil and I do not have proficiency in english.
The inequation is attached to the post. If you know how to answer the question or you know a video on YouTube who can help me learn, please send it to me. Thank you.
Attachments
20180410_105045-1.jpg
The inequation
20180410_105045-1.jpg (304.51 KiB) Viewed 260 times
Guest
 

Re: Calculus

Postby Guest » Thu Apr 12, 2018 4:48 am

[tex]\frac{36-3x}{x}>\frac{2-7x}{x}[/tex]

[tex]\frac{36-3x}{x}-\frac{2-7x}{x}>0[/tex]

[tex]\frac{36-3x- 2+7x}{x}>0[/tex]

[tex]\frac{4x+34}{x}>0[/tex]

First we need to find the root of the numenator
4x + 34 = 0
x = 17/2

So intervals are [tex](- \infty, 0), (0, 17/2), (17/2, \infty)[/tex]
Now let we check a value from the first interval and see if the expression will be positive or negative.
Let we take x = -1
[tex]\frac{4*(-1)+34}{-1} = \frac{30}{-1} < 0[/tex] - in this interval every value we take will give us a negative value

So solutions are only (0, 17/2)
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