- #1

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## Homework Statement

Solve for x

## Homework Equations

x^3 < x

## The Attempt at a Solution

x^3 < x

x^3 - x < 0

x(x^2 - 1) < 0

x(x+1)(x-1) < 0

For the expression on the left to be less than zero, it has to be two positives + negative or three negatives right? I've tried setting the different terms less than x, and greater than x but there's so many combinations and I get intervals with infinities which I can't make sense of.

What is a systematic/formal way of finding the solution set (and checking that it's right) without having to graph or doing it by trial and error?