Question

Решите системы неравенств

Answer 1

$1)\left \{ {{2x*6-\frac{x+1}{2}*6\leq \frac{x+1}{3}*6} \atop {(x+5)(x-3)+41\geq(x-6)^{2} }} \right.\\\\\left \{ {{12x-3(x+1)\leq2(x+1)} \atop {x^{2}-3x+5x-15+41\geq x^{2}-12x+36}} \right.\\\\\left \{ {{12x-3x-3\leq2x+2} \atop {2x+12x\geq 36+15-41}} \right.\\\\\left \{ {{7x\leq 5 } \atop {14x\geq 10}} \right.\\\\\left \{ {{x\leq \frac{5}{7}} \atop {x\geq \frac{5}{7}}} \right.\\\\Otvet:\boxed{\frac{5}{7}}$

$2)\left \{ {{\frac{2x-1}{4}*4-\frac{4-x}{2}*4>\frac{3}{4}*4} \atop {\frac{x-1}{2}*6<\frac{2-x}{3}*6+\frac{1}{2}*6}} \right.\\\\\left \{ {{2x-1-2(4-x)>3} \atop {3(x-1)<2(2-x)+3}} \right.\\\\\left \{ {{2x-1-8+2x>3} \atop {3x-3<4-2x+3}} \right.\\\\\left \{ {{4x>12} \atop {5x<10}} \right.\\\\\left \{ {{x>3} \atop {x<2}} \right. \\\\Otvet:\boxed{x\in\oslash}$