Question

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

Answer 1

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