# 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

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?

Is this the equation?

$\frac1x + 3< 0$
Guest

yes
Guest

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

$\frac{1 + 3x}{x} < 0$

First we solve $1+3x = 0$
$3x = -1$
$x = \frac{-1}{3}$

The intervals are $(-\infty; -\frac{1}{3}), (-\frac{1}{3}, 0)$ and $(0, +\infty)$

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

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

$(-\frac{1}{3}, 0)$
Guest

Is it clear?
Guest