Question

$3) left { {{ frac{x}{3} - frac{x}{4} textless frac{x}{6}-1}atop {6- frac{x}{2} textgreater frac{x}{4} +3}} right. 4) left { {{ frac{x}{5} - frac{2}{3} textless frac{2}{5}- frac{x}{3} }atop {frac{2}{7}+ frac{x}{3} textgreater frac{x}{7}- frac{2}{3} }} right.$

Answer 1

$3) left { {{ frac{x}{3} - frac{x}{4} textless frac{x}{6}-1}atop {6- frac{x}{2} textgreater frac{x}{4} +3}} right.$
$left { {{ frac{4x}{12} - frac{3x}{12} textless frac{2x-12}{12}}atop { frac{24-2x}{4} textgreater frac{x+12}{4} }} right. \ \left { {{ frac{x}{12} textless frac{2x-12}{12}}atop { frac{24-2x}{4} textgreater frac{x+12}{4} }} right. \ \ left { {{x textless 2x-12} atop {24-2x textgreater x+12}} right. \ \ left { {{-x textless -12} atop {-3x textgreater -12}} right. \ \ left { {{x textgreater 12} atop {x textless 4}} right.$
Система не имеет решений
$4) left { {{ frac{x}{5} - frac{2}{3} textless frac{2}{5}- frac{x}{3} }atop {frac{2}{7}+ frac{x}{3} textgreater frac{x}{7}- frac{2}{3} }} right.$
$left { {{ frac{3x}{15} - frac{10}{15} textless frac{6}{15}- frac{5x}{15} }atop {frac{6}{21}+ frac{7x}{21} textgreater frac{3x}{21}- frac{14}{21} }} right.$
$left { {{ frac{3x-10}{15} textless frac{6-5x}{15} }atop {frac{6+7x}{21} textgreater frac{3x-14}{21} }} right. \ \ left { {{3x-10 textgreater 6-5x} atop {6+7x textgreater 3x-14}} right. \ \ left { {{8x textgreater 16} atop {4x textless 20}} right. \ \ left { {{x textgreater 2} atop {x textless 5}} right. \ \ 2 textless x textless 5$
Ответ. (2;5)