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

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

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Answer 1 · 2016-10-22T15:58:25

$x ∈)-oo,0(∪)0,1 ($

Explanation:

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

on factorization, $x^2(x-1)<0$

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

here is the sign chart

$x$ $color(white(aaaaaa))$ $-oo$ $color(white)(aaaa)$ $0$ $color(white)(aaaaaaaaa)$ $1$ $color(white)(aaaaaa)$ $+oo$
$x$ $color(white)(aaaaa)$ $-$ $color(white)(aa)$ $0$ $color(white)(aaaa)$ $+$ $color(white)(aaaaaaa)$ $+$
$x^2$ $color(white)(aaaa)$ $+$ $color(white)(aa)$ $0$ $color(white)(aaaa)$ $+$ $color(white)(aaaaaaa)$ $+$
$x-1$ $color(white)(aa)$ $-$ $color(white)(aa)$ $color(white)(aaaaa)$ $-$ $color(white)(aaa)$ $0$ $color(white)(aa)$ $color(white)(aa)$ $+$ $color(white)(aaa)$
$x^2(x-1)$ $-$ $color(white)(aaaaa)$ $-$ $color(white)(aaaaaaaaa)$ $+$

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

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

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