Question

How do you solve `x^2-4x<-3` using a sign chart?

Answer 1

The answer is `x in ] 1,3 [`

Explanation:

Rewrite the equation as, `x^2-4x+3<0`

Let `f(x)=x^2-4x+3=(x-1)(x-3)`

The domain of `f(x)` is `D_f(x)=RR`

Now, we can do our sign chart

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

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

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

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

So,

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