Question

Potrzebuję rozwiązania nierówności (bez osi liczbowej)

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

Dziękuję :)

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

9x<33

x<33/9

x<11/3

 

b)

(2x-3)(3x+5)-(x+2)(6x-1)≤ 2

6x²+10x-9x-15-(6x²-x+12x-2)≤2

6x²+x-15-6x²+x-12x+2≤2

-10x≤15

x≥-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

3x²-6x+15x-30-5x≥2x+3x²+4

2x≥34

x≥17

 

d)

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

-2(6x-3-2x²+x)-(-6x+12+4x²-8x)>3x-6

-12x+6+4x²-2x+6x-12-4x²+8x>3x-6

-3x>0

x<0 

 

 

 

 

 

 

Answer 2

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

11x+15x-5x-12x < 15+18

9x < 33 |:9

x < 33/9

x < 11/3

x < 3 ⅔

 

b)

(2x-3)(3x+5)-(x+2)(6x-1) ≤ 2

6x²+10x-9x-15-(6x²-x+12x-2) ≤ 2

6x²+x-15-6x²+x-12x+2 ≤ 2

x+x-12x ≤ 2-2+15

-10x ≤ 15 |:(-10)

x ≥ -15/10

x ≥ -3/2

x ≥ -1½

 

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-3-2x²+x)-(-6x+12+4x²-8x) > 3x-6

-12x+6+4x²-2x+6x-12-4x²+8x > 3x-6

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

-3x > 0 |:(-3)

x < 0