How do you solve an inequality that has a fraction 1/x+3< 0

How do you solve an inequality that has a fraction 1/x+3< 0

Postby Guest » Sun Jul 29, 2018 4:04 am

Hi there,
i was hoping someone would be able to help me with an inequality that i have come across.
1/x+3< 0
Any help would be appreciated as I cannot find out how to solve this anywhere on the internet.

thank you.
Guest
 

Re: how do you solve an inequality that has a fraction < 0?

Postby Guest » Sun Jul 29, 2018 10:37 am

Is this the equation?

[tex]\frac1x + 3< 0[/tex]
Guest
 

Re: how do you solve an inequality that has a fraction < 0?

Postby Guest » Sun Jul 29, 2018 10:42 pm

yes
Guest
 

Re: How do you solve an inequality that has a fraction 1/x+3

Postby Guest » Mon Jul 30, 2018 3:28 am

[tex]\frac{1 + 3x}{x} < 0[/tex]

First we solve [tex]1+3x = 0[/tex]
[tex]3x = -1[/tex]
[tex]x = \frac{-1}{3}[/tex]

The intervals are [tex](-\infty; -\frac{1}{3}), (-\frac{1}{3}, 0)[/tex] and [tex](0, +\infty)[/tex]

Now we choose a random number from the last interval let it be for example 1
the equation
becomes [tex]\frac{1}{1}+3 > 0[/tex]

So numbers in the intervals [tex](0, +\infty)[/tex] and [tex](-\infty; -\frac{1}{3})[/tex] are positive and
solutions are numbers within the interval

[tex](-\frac{1}{3}, 0)[/tex]
Guest
 

Re: How do you solve an inequality that has a fraction 1/x+3

Postby Guest » Mon Jul 30, 2018 3:29 am

Is it clear?
Guest
 


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