Question

найдите целые решения системы неравенств
{5x-1>2x+4
{x(x-6)-(x+2)(x-3) ≥x-30

Answer 1

$\displaystyle\left \{ {{5x-1>2x+4} \atop {x(x-6)-(x-2)(x-3)\geq x-30}} \right.\\\\\\\displaystyle\left \{ {{5x-2x>4+1} \atop {x^{2} -6x-x^{2} +5x-6\geq x-30}} \right. \\\\\\\displaystyle\left \{ {{3x>5} \atop {-x-x\geq -30+6}} \right. \\\\\\\displaystyle\left \{ {{x>1\dfrac{2}{3} } \atop {-2x\geq -24}} \right. \\\\\\\displaystyle\left \{ {{x>1\dfrac{2}{3} } \atop {x\leq 12}} \right. \\\\\\Otvet:\boxed{x\in\Big(1\frac{2}{3} \ ; \ 12\Big]}$