Question

Решите неравенство:
$\frac{x-1}{x+5}\geq 2$

Answer 1

$\frac{x-1}{x+5} \geq 2,x\neq -5\\\frac{x-1}{x+5} -2\geq 0\\\frac{x-1-2(x+5)}{x+5} \geq 0\\\frac{x-1-2x-10}{x+5} \geq 0\\\frac{-x-11}{x+5} \geq 0\\\left \{ {{x\leq-11 }\atop{x>-5}} \right. \\\left \{ {{x\geq -11} \atop {x<-5}} \right.$

$x$∈∅

$x$∈[ $-11,-5$⟩

$x$∈ [$-11,-5$⟩,$x\neq -5$

Ответ:$x$∈[ $-11,-5$⟩