Question

How do you solve `(x-1)(3x-4)>=0` using a sign chart?

Answer 1

The answer is `x in ] -oo,1 ] uu [ 4/3, +oo[`

Explanation:

Let `f(x)=(x-1)(3x-4)`

Let's do the sign chart

`color(white)(aaaa)` `x` `color(white)(aaaa)` `-oo` `color(white)(aaaa)` `1` `color(white)(aaaa)` `4/3` `color(white)(aaaa)` `+oo`

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

`color(white)(aaaa)` `3x-4` `color(white)(aaaa)` `-` `color(white)(aaa)` `-` `color(white)(aaaa)` `+`

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

So, `f(x)>=0` for `x in ] -oo,1 ] uu [ 4/3, +oo[`

graph{y=(x-1)(3x-4) [-1.863, 3.006, -1.232, 1.2]}