Question

zad1.
a)5(x-2)+6<12(x+1)+5
b)20(1-2x)+1>7(x+14)
c)4(2x-3)+3(5x-2)<8(x+1)-9(x+4)-14
d)2(x-3)+3(x-4)+4(x-5)+5(x-6)+6(x-7)<0

Answer 1

a)

5(x-2)+6<12(x+1)+5

5x-10+6 < 12x+12+5

5x-4 < 12x+17

5x-12x < 17+4

-7x < 21 /:(-7)

x > -3

b)

20(1-2x)+1>7(x+14)

20-40x+1 > 7x+98

21-40x > 7x+98

-40x-7x > 98-21

-47x > 77 /:(-47)

x <  -77/47

x < -1 30/47

c)

4(2x-3)+3(5x-2)<8(x+1)-9(x+4)-14

8x-12+15x-6 < 8x+8-9x-36-14

23x-18 < -x-42

23x+x < -42+18

24x < -24/:24

x > -1

d)

2(x-3)+3(x-4)+4(x-5)+5(x-6)+6(x-7)<0

2x-6+3x-12+4x-20+5x-30+6x-42 < 0

20x-110 < 0

20x < 110/:20

x < 5,5

Answer 2

Zadanie 1.

a)5(x-2)+6<12(x+1)+5

5x-10+6<12x+12+5

5x-12x<12+5-6+10

-7x<21/:(-7)

x<-3

b)20(1-2x)+1>7(x+14)

20-40x+1>7x+98

-40x-7x>98-20-1

-47x>-77/(-47)

x>77/47

x> 1 i 30/47

c)4(2x-3)+3(5x-2)<8(x+1)-9(x+4)-14

6x-12+15x-6<8x+8-9x-36-14

6x+15x-8x+9x<8-36-14+12+6

23x-18<-x-42

23x+x<-42+18

24x<-24/:24

x>-1

d)2(x-3)+3(x-4)+4(x-5)+5(x-6)+6(x-7)<0

2x-6+3x-12+4x-20+5x-30+6x-42<0

2x+3x+4x+5x+6x<42+6+12+20+30

20x<110/:20

x<5,5