# A really simple inequality, easy to see the solution but hard to prove algebraically.

1. Dec 17, 2012

### brownman

1. The problem statement, all variables and given/known data

Solve the inequality -9 < 1/x

A simple inequality, I can see the solution is just x < -1/9 but I can't prove it at all.

3. The attempt at a solution

-9 < 1/x

-9x < 1

x > -1/9

Any helpful rules I am forgetting about inequalities? This was a problem in a review from high school set provided by my instructor for my introductory math class. Just curious about a solution, it's a calculus course that doesn't really test on this sort of thing but I figure I should actually try and figure out these basic things.

Last edited: Dec 17, 2012
2. Dec 17, 2012

### Dick

Re: A really simple inequality, easy to see the solution but hard to prove algebraica

You are forgetting if you multiply both sides by x and x is negative you have to reverse the inequality. Split into two cases x>0 and x<0.

3. Dec 17, 2012

### brownman

Re: A really simple inequality, easy to see the solution but hard to prove algebraica

Oh okay, that makes sense, thanks for the help :).