Verified answer

Ответ:

1)  x ∈ (6;  +∞)

2) x ∈ (-∞; 2,4)

3) x ∈ ∅

Пошаговое объяснение:

[tex]\displaystyle \left \{ {{2x-12 > 0} \atop {3x > 9\hfill}} \right. \left \{ {{2x > 12} \atop {x > 3\hfill}} \right. \left \{ {{x > 6 } \atop {x > 3}} \right. \quad \Rightarrow x\in(6;+\infty)[/tex]

[tex]\displaystyle \left \{ {{57-7x > 3x-2} \atop {22x-1 < 2x+47}} \right. \left \{ {{57+2 > 3x+7x} \atop {22x-2x < 47+1}} \right. \left \{ {{10x < 59} \atop {20x < 48}} \right. \left \{ {{x < 5,9} \atop {x < 2,4}} \right. \quad \Rightarrow \quad x\in(-\infty; 2,4)[/tex]

[tex]\displaystyle \left \{ {{\displaystyle\frac{x-1}{2}-\frac{x-3}{3} < 2 } \atop {\displaystyle\frac{13x-1}{2} > 0\hfill}} \right. \left \{ {{3(x-1)-2(x-3) < 2} \atop {13x-1 > 0\hfill}} \right. \left \{ {{x < -1} \atop {\displaystyle x > \frac{1}{13} }} \right. \Rightarrow x\in \emptyset[/tex]