Question

Rozwiąż nierówności :
a)(x-3)(7-5x)+3-11x <-5(x-1)(x+3)+12x
b) ( 2x-3)(3x+5)-(x+2)(6x-1)< 2
c) 3(x+5)(x-2)-5x > (3x-1)(1+x)+5
d) -2(3-x)(2x+1)-(3-2x)(-2x+4)>3x-6

Answer 1

A) (x-3)(7-5x)+3-11x <-5(x-1)(x+3)+12x =
7x-5x²-21+15x+3-11x< -5(x²+3x-x-3)+12x=
-5x²+11x-18<-5(x²+2x-3)+12x=
-5x²+11x-18<-5x²-10x+15+12x=
-5x²+11x-18<-5x²+2x+15=
-5x²+11x-18+5x²-2x-15<0
9x-33<0
9x<33/9
x<3⅔

b)( 2x-3)(3x+5)-(x+2)(6x-1)< 2
(6x²+10x-9x-15)-(6x²-x+12x-2)<2
6x²+x-15-6x²-11x+2<2
-10x-13-2<0
-10x<15/:(-10)
x=-³/₂

c)3(x+5)(x-2)-5x > (3x-1)(1+x)+5
3(x²-2x+5x-10)-5x>3x+3x²-1-x+5
3(x²+3x-10)-5x>3x²-2x+4
3x²+9x-30-5x>3x²-2x+4
3x²+4x-30>3x²-2x+4
3x²+4x-30-3x²+2x-4>0
6x-34>0
6x>34
x=5⅔

d)-2(3-x)(2x+1)-(3-2x)(-2x+4)>3x-6
-2(6x+3-2x²-x)-(-6x+12+4x²-6x>3x-6
-2(5x+3-2x²)-(-12x+12+4x²)>3x-6
-10x-6+4x²+12x-12-4x²>3x-6
-10x-6+4x²+12x-12-4x²-3x+6>0
-x-12>0
-x>12/:(-1)
x>-12