Question

Розв’язати систему нерівностей

Answer 1

$\displaystyle\bf\\\left \{ {{\dfrac{2x-1}{4} -\dfrac{4-x}{2} > \dfrac{3}{4} } \atop {\dfrac{x-1}{2} < \dfrac{2-x}{3} +\dfrac{1}{2} }} \right. \\\\\\\left \{ {{\dfrac{2x-1}{4}\cdot 4 -\dfrac{4-x}{2} \cdot 4 > \dfrac{3}{4} \cdot 4} \atop {\dfrac{x-1}{2}\cdot 6 < \dfrac{2-x}{3} \cdot 6+\dfrac{1}{2} \cdot 6}} \right. \\\\\\\left \{ {{2x-1-2\cdot(4-x) > 3} \atop {3\cdot(x-1) < 2\cdot(2-x)+3}} \right. \\\\\\\left \{ {{2x-1-8+2x > 3} \atop {3x-3 < 4-2x+3}} \right.$

$\displaystyle\bf\\\left \{ {{4x > 3+1+8} \atop {3x+2x < 4+3+3}} \right. \\\\\\\left \{ {{4x > 12} \atop {5x < 10}} \right. \\\\\\\left \{ {{x > 3} \atop {x < 2}} \right. \\\\\\Otvet \ : \ x\in\oslash$