Question

Решите систему неравенств: 1)5x-20<0 2)2x+40>30
3x+18>0 21-4x<5

Answer 1

1)

$\displaystyle \left \{ {{5x-20<0} \atop {3x+18>0}} \right.\\\\\left \{ {{5x<20} \atop {3x>-18}} \right.\\\\\left \{ {{x<20:5} \atop {x> -18:3}} \right.\\\\\left \{ {{x<4} \atop {x>-6}} \right.$

x<4   __\\\\\\\\\\\\\ -6 __\\\\\\\\\\\\\\\ 4__________

x> -6                                  //////////////////////////////////

Ответ: (-6; 4)

2)

$\displaystyle \left \{ {{2x+40>30} \atop {21-4x<5}} \right. \\\\\left \{ {{2x>30-40} \atop {-4x<5-21}} \right.\\\\\left \{ {{2x> -10} \atop {-4x<-16}} \right.\\\\ \left \{ {{x>-5} \atop {-x< -4}} \right.\\\\\left \{ {{x>-5} \atop {x>4}} \right.$

x> -5 _______-5 _\\\\\\\\\\\__4__\\\\\\\\\\__

x>4                                                  //////////

Ответ: (4;+∞)