Question

How do you solve `(x-4)(x+1)>=0` using a sign chart?

Answer 1

The answer is `x in ] -oo,-1 [ uu [4, +oo[`

Explanation:

Let `f(x)=(x-4)(x+1)`

Let's do the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `-1` `color(white)(aaaa)` `4` `color(white)(aaaa)` `+oo`

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

`color(white)(aaaa)` `x-4` `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 ] -oo,-1 [ uu [4, +oo[`

graph{(x-4)(x+1) [-12.66, 12.65, -6.33, 6.33]}