Solving an Inequality: -9 < 1/x

[brownman]

Homework Statement

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.

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.

 

[Dick]

Homework Statement

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.

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, I have no

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.

 

[brownman]

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