Question

N 609. ПОМОГИТЕ РЕШИТЬ.
Система неравенств​

Answer 1

$1); ; left{begin{array}{l}x^2-x-2<0\5-2x<0end{array}right; ; left{begin{array}{l}(x-2)(x+1)<0\2x>5end{array}right; ; left{begin{array}{l}-1<x<2\x>2,5end{array}right; ; xin varnothing \\\2); ; left{begin{array}{l}4+3x-x^2>0\2-x>0end{array}right; ; left{begin{array}{l}x^2-3x-4<0\2>xend{array}right; ; left{begin{array}{l}(x-4)(x+1)<0\x<2end{array}right\\\left{begin{array}{l}-1<x<4\x<2end{array}right; ; Rightarrow ; ; ; xin (-1, ;, 2)$

$3); ; left{begin{array}{l}x^2-8x+15<0\frac{1}{2}, x+1geq 3end{array}right; ; left{begin{array}{l}(x-3)(x-5)<0\x+2geq 6end{array}right; ; left{begin{array}{l}3<x<5\xgeq 4end{array}right; ; ; Rightarrow\\\xin [; 4, ;, 5, )$

$4); ; left{begin{array}{l}-x^2+6x-8<0\4x-3leq 0end{array}right; ; left{begin{array}{l}x^2-6x+8>0\4xleq 3end{array}right; ; left{begin{array}{l}(x-2)(x-4)>0\xleq 0,75end{array}right\\\left{begin{array}{l}xin (-infty ;2)cup (4;+infty )\xin (-infty , ;; 0,75; ]end{array}right; ; Rightarrow quad xin (-infty , ;, 0,75; ]$