# How do you solve  x/2>1+(4/x)?

May 29, 2016

x is outside $\left[4 , - 2\right]$

#### Explanation:

x cannot be 0.

Multiply throughout by 2x and rearrange. The inequality sign is

reversed, when x is negative. Accordingly,

x^2-2x-8 > < 0, respectively.

${\left(x - 1\right)}^{2} > < 9$. So, x-1 > < +- 3>

In the first case, x > 0, and so, x > 4; the other inequality is

When x is negative, $x < - 2$; the other inequality is inadmissible.
So, $x < - 2 \mathmr{and} x > 4$