Question

Помогите решить линейные неравенства

Answer 1

1. {2x > 2

{ x < 3

___

{x > 1

{x < 3

Ответ: x ∈ (1; 3)

2.

{2x > 8

{3x < 12

___

{x > 4

{x < 4

нет корней

3.

{x > 2

{x < 3

Ответ: x ∈ (2; 3)

Answer 2

$1)\; \; \left \{ {{2x-1>1} \atop {3-x>0}} \right. \; \left \{ {{2x>2} \atop {3>x}} \right. \; \left \{ {{x>1} \atop {x<3}} \right. \; \; \Rightarrow \; \; 1<x<3\\\\2)\; \; \left \{ {{1-2x<-9} \atop {3x+1<13}} \right. \; \left \{ {{-2x<-10} \atop {3x<12}} \right. \; \left \{ {{x>5} \atop {x<4}} \right. \; \; \Rightarrow \; \; x\in \varnothing$

$3)\; \; \left \{ {{3x+7>9+2x} \atop {5+x>2x+2}} \right. \; \left \{ {{3x-2x>9-7} \atop {5-2>2x-x}} \right. \; \left \{ {{x>2} \atop {3>x}} \right. \; \left \{ {{x>2} \atop {x<3}} \right. \; \; \Rightarrow \; \; 2<x<3$