$\displaystyle 1 + l x l > \frac{6}{l x l}$

lxl stands for modulus of x. Find the solution set

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- Jun 15th 2009, 08:42 AMmark1950[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 AMstapel
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 AMPlato