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 < -5x2-15x+5x+15+12x

-5x2+11x-18 < -5x2+2x+15

11x-2x < 15+18

9x < 33 |:9

x < 33/9

x < 3 i 2/3

 

b)(2x-3)(3x+5)-(x+2)(6x-1)</ 2

6x2+10x-9x-15-(6x2-x+12x-2) </ 2

6x2+10x-9x-15-6x2+x-12x+2 </ 2

10x-9x+x-12x </ 2+15-2

-10x </ 15 |:(-10)

x /> -1,5

c)3(x+5)(x-2)-5x/>(3x-1)(1+x)+5

3(x2-2x+5x-10)-5x /> 3x+3x2-1-x+5

3x2-6x+15x-30-5x /> 3x+3x2-1-x+5

-6x+15x-5x-3x+x />-1+5+30

2x /> 34 |:2

x /> 17

 

 

d)-2(3-x)(2x-1)-(3-2x)(-2x+4) > 3x-6

-2(6x-3-2x^2+x)-(-6x+12+4x^2-8x) > 3x-6

-12x+6+4x^2-2x+6x-12-4x^2+8x > 3x-6

-12x-2x+6x+8x-3x > -6-6+12

-3x > 0 |:(-3)

x < 0

Answer 2

Rozwiązanie w załączniku.

Answer 3

A)(x-3)(7-5x)+3-11x<-5(x-1)(x+3)+12x
7x-5x2-21+15x+3-11x<-5(x2+3x-1x-3)+12x
7x-5x2-21+15x+3-11x<-5x2-15x+5x+15+12x
7x-5x2+15x-11x+5x2+15x-5x-12x<21-3-15
9x<3 /:9
x<1/3

b)(2x-3)(3x+5)-(x+2)(6x-1)</ 2
6x2+10x-9x-15-6x2+1x-12x+2</2
6x2+10x-9x-6x2+1x-12x</2+15-2
-10x</15 /: (-10)
x/>-1,5

c)3(x+5)(x-2)-5x/>(3x-1)(1+x)+5
3(x2-2x+5x-10)-5x/>3x+3x2-2-1x+5
3x2-6x+15x-30-5x/>3x+3x2-2-1x+5
3x2-6x+15x-5x-3x-3x2+1x/>30-2
2x/>18 /:2
x/>9

d)-2(3-x)(2x-1)-(3-2x)(-2x+4)>3x-6
-2(6x-3-2x2+1x)+6x-12-4x2+8x>3x-6
-12x+6+4x2-2x+6x-12-4x2+8x>3x-6
-12x+4x2-2x+6x-4x2+8x-3x>-6-6+12
-3x>0
x>0