Question

Решить совокупности неравенств.

2) {-1≤x<0

0≤x<2

2≤x<5


3) $\frac{3-2x}{5}$ ≤ $\frac{1-x}{2}$

2-3x>x

Answer 1

Ответ:  $1)\; \; \varnothing \; ,\; \; 2)\; \; x\in (-\infty ,-1\, ]\; .$

Объяснение:

$1)\; \; \left \{ {{-1\leq x<0} \atop {0\leq x<2\; \; ,\; \; 2\leq x<5}} \right. \; \; \Rightarrow \; \; \; x\in [-1,0)\cap [\, 0,2)\cap [\, 2,5)=\varnothing \\\\\\2)\; \; \left \{ {{\frac{3-2x}{5}\leq \frac{1-x}{2}} \atop {2-3x>x}} \right.\; \; \left \{ {{6-4x\leq 5-5x} \atop {4x<2}} \right.\left \{ {{x\leq -1} \atop {x<\frac{1}{2}}} \right.\; \; \; \Rightarrow \; \; x\leq -1\\\\x\in (-\infty ,-1\; ]\\\\\\P.S.\; \; \left [ {{-1\leq x<0} \atop {0\leq x<2\; \; ,\; \; 2\leq x<5}} \right. \; \; \Rightarrow \; \; \; x\in [-1,0)\cup [\, 0,2)\cup [\, 2,5)=[-1,5)$

$\left [ {{x\leq -1} \atop {x<\frac{1}{2}}} \right.\; \; \Rightarrow \; \; \; x<\frac{1}{2}\; \; ,\; \; x\in (-\infty ,\frac{1}{2}\, )$