Question

решите систему уравнений 5(2х+3)-2(5х+3)>3х
(х-6)(х+2)<х² РЕШИТЕ ПОЖАЛУЙСТА

Answer 1

$\left \{ {{5(2x+3)-2(5x+3)>3x} \atop {(x-6)(x+2)<x^2}} \right.$

$\left \{ {{10x+15-10x-6>3x} \atop {x^2-6x+2x-12<x^2}} \right.$

$\left \{ {{9>3x} \atop {x^2-4x-12<x^2}} \right.$

$\left \{ {{9-3x>3x-3x} \atop {x^2-4x-12-x^2<x^2-x^2}} \right.$

$\left \{ {{9-3x>0} \atop {-4x-12<0}} \right.$

$\left \{ {{9-3x-9>0-9} \atop {-4x-12+12<0+12}} \right.$

$\left \{ {{-3x>-9} \atop {-4x<12}} \right.$

$\left \{ {{-3x*(-1)<-9*(-1)} \atop {-4x*(-1)>12*(-1)}} \right.$

$\left \{ {{3x<9} \atop {4x>-12}} \right.$

$\left \{ {{3x:3<9:3} \atop {4x:4>-12:4}} \right.$

$\left \{ {{x<3} \atop {x>-3}} \right.$

$-3<x<3$

Ответ: x∈(-3;  3)