# [SOLVED] How to solve this inequation?

• Jun 15th 2009, 08:42 AM
mark1950
[SOLVED] How to solve this inequation?
$\displaystyle 1 + l x l > \frac{6}{l x l}$

lxl stands for modulus of x. Find the solution set
• Jun 15th 2009, 09:19 AM
stapel
Consider cases. Obviously, x cannot equal zero, or you'll have division by zero.

If x > 0, then |x| = x, and you have 1 + x > 6/x, so x^2 + x - 6 > 0.

If x < 0, then |x| = -x, and you have 1 - x > -6/x, so 0 < x^2 - x - 6.

Solve the two quadratic inequalities. (Wink)
• Jun 15th 2009, 09:30 AM
Plato
Quote:

Originally Posted by mark1950
$\displaystyle 1 + l x l > \frac{6}{l x l}$
lxl stands for modulus of x. Find the solution set

Here is a second way.
That is $\displaystyle |x|+|x|^2>6$ then it follows that $\displaystyle |x|>2$.
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