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Mush · #2 January 12th, 2009, 06:04 PM

Quote:

Originally Posted by Random-Hero-

How would I go about solving
(1/x) + 4 < 2/x?

Any help would be greatly appreciated!!

$\frac{1}{x} + 4 < \frac{2}{x}$

Subtract $\frac{2}{x}$ from both sides!

$\frac{1}{x} + 4 - \frac{2}{x} < 0$

Subtract 4 from both sides!

$\frac{1}{x} - \frac{2}{x} < -4$

Now you have to re-write the LHS as a single fraction, which is easy since they have the same denominator!

$\frac{1-2}{x} < -4$

$\frac{-1}{x} < -4$

Now if you multiply through by negative 1, you'll get a nicer expression, but remember that when you multiply through by negative 1, the direction of the inequality changes!

$\frac{1}{x} > 4$

Can you draw any conclusions from this?