How do you solve x^3<x^2 using a sign chart?

Oct 22, 2016

x ∈)-oo,0(∪)0,1 (

Explanation:

Rewrite the equation as ${x}^{3} - {x}^{2} < 0$

on factorization, ${x}^{2} \left(x - 1\right) < 0$

the points we have to look at are $x = 0$ and $x = 1$

here is the sign chart

$x$ color(white(aaaaaa)) $- \infty$ $\textcolor{w h i t e}{a a a a}$ $0$ $\textcolor{w h i t e}{a a a a a a a a a}$ $1$ $\textcolor{w h i t e}{a a a a a a}$ $+ \infty$
$x$$\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a}$ $0$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a a a a}$$+$
${x}^{2}$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a}$ $0$$\textcolor{w h i t e}{a a a a}$$+$$\textcolor{w h i t e}{a a a a a a a}$$+$
$x - 1$$\textcolor{w h i t e}{a a}$$-$$\textcolor{w h i t e}{a a}$ $\textcolor{w h i t e}{a a a a a}$$-$$\textcolor{w h i t e}{a a a}$$0$$\textcolor{w h i t e}{a a}$ $\textcolor{w h i t e}{a a}$$+$$\textcolor{w h i t e}{a a a}$
${x}^{2} \left(x - 1\right)$$-$$\textcolor{w h i t e}{a a a a a}$ $-$$\textcolor{w h i t e}{a a a a a a a a a}$$+$

So the answer is x ∈)-oo,0(∪)0,1 ( for $x < 0$