Решите неравенства:
1) 2(1-x)>=5x-(3+2)
2) 7x+3>5(x-4)+1
3) x^2-9>0
4) x^2-11x+30<=0
5) -2x^2+5x-2<0
6) (2x+3)(x-1)<0
7) x(4-x)(x+1)>=0
8) (2x-4)/(-x+5)>=0
()/()-дробь
1) 2(1-x)>=5x-(3+2)
2) 7x+3>5(x-4)+1
3) x^2-9>0
4) x^2-11x+30<=0
5) -2x^2+5x-2<0
6) (2x+3)(x-1)<0
7) x(4-x)(x+1)>=0
8) (2x-4)/(-x+5)>=0
()/()-дробь
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Verified answer
1) 2(1-x)>=5x-(3+2)2 - 2x >= 5x - 3 - 2
-7x>=-7
x<=1
2) 7x+3>5(x-4)+1
7x + 3 > 5x - 20 + 1
2x > -22
x>-11
3) x^2-9>0
x^2 > 9
x>3
or
x<-3
4) x^2-11x+30<=0
D = 121 - 120 = 1
x1 = (11+1)/2 = 6 => x <= 6
x2 = (11-1)/2= 5 => x>=5 => 5<=x<=6
5) -2x^2+5x-2<0
D = 25 - 16 =9
x1 = (-5+3)/(-4) = 0,5 => x<0,5
x2 = (-5-3)/(-4) = 2 => x>2
6) (2x+3)(x-1)<0
{+} {+}
-------------o-----------o------->x
-1,5 {-} 1
-1,5<x<1
7) x(4-x)(x+1)>=0
{+} {+}
---------|-------|-------|----->x
-1 {-} 0 4 {-}
x<=-1 and 0 <= x <=4
8) (2x-4)/(-x+5)>=0
{+} {+}
--------o--------|------>x
-5 {-} 2
-5 < x <= 2