2x-8/2x-4≥3 как решить?

2х-4 ≠0 ⇒2х≠4 ⇒ х≠2

$\frac{2x-8}{2x-4} \geq 3 \\ \\ \frac{2x-8}{2x-4} -3 \geq 0 \\ \\ \frac{2x-8-3*(2x-4)}{2x-4} \geq 0 \\ \\ \frac{2x-8-6x+12}{2x-4} \geq 0 \\ \\ \frac{-4x+4}{2x-4} \geq 0 \\ \\ \frac{4(1-x)}{2(x-2)} \geq 0 \\ \\ \frac{1-x}{x-2} \geq 0 \\ \\ \left \{ {{1-x \leq 0} \atop {x-2 \ \textless \ 0}} \right. \\ \\ \left \{ {{x \geq 1} \atop {x \ \textless \ 2}} \right. \\ \\ 1 \leq x \ \textless \ 2 \\ \\ \left \{ {{1-x \geq 0} \atop {x-2\ \textgreater \ 0}} \right. \\ \\ \left \{ {{x \leq 1} \atop {x\ \textgreater \ 2}} \right.$

решений нет

Ответ : 1 ≤ x < 2.