Question

970 решите системы неравенств.

Answer 1

Ответ:

$\displaystyle \tt 1) \; \; \left \{ {{3(x-1)<x-3} \atop {5(x+3)>2x+3}} \right. \Leftrightarrow \left \{ {{3x-3<x-3} \atop {5x+15>2x+3}} \right. \Leftrightarrow \left \{ {{2x<0} \atop {3x>-12}} \right. \Leftrightarrow \\\\\Leftrightarrow \left \{ {{x<0} \atop {x>-4}} \right. \Leftrightarrow x \in (-4; 0);$

$\displaystyle \tt 2) \; \; \left \{ {{2(y-2)\geq 3y+1} \atop {5(y+1)\leq 4y+3}} \right. \Leftrightarrow \left \{ {{2y-4 \geq 3y+1} \atop {5y+5 \leq 4y+3}} \right. \Leftrightarrow \left \{ {{-y \geq 5} \atop {y \leq -2}} \right. \Leftrightarrow \\\\\Leftrightarrow \left \{ {{y \leq -5} \atop {y \leq -2}} \right. \Leftrightarrow y \in (-\infty; -5];$

$\displaystyle \tt 3) \; \; \left \{ {{3(2y-3)\leq y+6} \atop {4(3y+1) \geq 5y-10}} \right. \Leftrightarrow \left \{ {{6y-9\leq y+6} \atop {12y+4 \geq 5y-10}} \right. \Leftrightarrow \left \{ {{5y\leq 15} \atop {7y \geq -14}} \right. \Leftrightarrow \\\\\Leftrightarrow \left \{ {{y\leq 3} \atop {y \geq -2}} \right. \Leftrightarrow y \in [-2; 3];$

$\displaystyle \tt 4) \; \; \left \{ {{2(3x+2)>5(x-1)} \atop {7(x+2)<3(2x+3)}} \right. \Leftrightarrow \left \{ {{6x+4>5x-5} \atop {7x+14<6x+9}} \right. \Leftrightarrow \left \{ {{x>-9} \atop {x<-5}} \right. \Leftrightarrow x \in(-9;-5).$