# How do you solve (x+4)/x>0?

Apr 10, 2018

Either $x > 0$ or $x < - 4$

#### Explanation:

We can multiply both sides of the inequality by ${x}^{2}$ to get

$x \left(x + 4\right) > 0$

Note that we multiply by ${x}^{2}$ since it is always positive and multiplying by a positive quantity does not change the sign of the inequality (on the other hand, multiplying by $x$ would have lead apparently to $x + 4 < 0$, which is wrong!)

Now, for $x \left(x + 4\right) > 0$, either both factors have to be positive, or both have to be negative. In the first case, $x$ has to be greater than 0, in the second, it has to be smaller than -4.