Question

How do you solve `x(x-1)(x+3) <0`?

Answer 1

The answer is `x in ] -oo,-3 [ uu] 0,1 [`

Explanation:

Let `f(x)=x(x-1)(x+3)`

Let's do a sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-3` `color(white)(aaaa)` `0` `color(white)(aaaa)` `1` `color(white)(aaaa)` `+oo`

`color(white)(aaaa)` `x+3` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaa)` `+` `color(white)(aaa)` `+`

`color(white)(aaaa)` `x` `color(white)(aaaaaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaa)` `+` `color(white)(aaa)` `+`

`color(white)(aaaa)` `x-1` `color(white)(aaaaa)` `-` `color(white)(aaaa)` `-` `color(white)(aaa)` `-` `color(white)(aaa)` `+`

`color(white)(aaaa)` `f(x)` `color(white)(aaaaaa)` `-` `color(white)(aaaa)` `+` `color(white)(aaa)` `-` `color(white)(aaa)` `+`

`f(x)<0` when, `x in ] -oo,-3 [ uu] 0,1 [`

graph{x(x-1)(x+3) [-7.9, 7.9, -3.95, 3.95]}