Question

Rezolvați ecuațiile:
a) 3(2x-5)+4(x-7)=3(4x+11)-85
b) 3[2(x-4)-3(x-5)]=4[3(x+2)-4(x+1)]+15
c) 3[8-5(3x-2)]+4(4x-9)=2[3(2x-5)+28]-49
d) 2[3(x+1)-4((2x-3)]-18=11-3[2(3x-5)-3(x+4)]
e) 25-4[6(x+1)-3(3x+4)]=5[2(3x-7)-3(x-5)]+23

Answer 1

a)

3(2x-5)+4(x-7)=3(4x+11)-85⇒6x-15+4x-28=12x+33-85

10x - 43 = 12x - 52⇒-43 + 52 = 12x -10x

9 = 2x⇒x = 9/2

b)

3[2(x-4)-3(x-5)]=4[3(x+2)-4(x+1)]+15

3(2x-8-3x+15)=4(3x+6-4x-4)+15⇒3(7-x)=4(2-x)+15

21-3x=8-2x+15⇒21 - 8 - 15 = - 2x +3x⇒x = -2

c)

3[8-5(3x-2)]+4(4x-9)=2[3(2x-5)+28]-49

3(8-15x+10)+16x-36=2[(6x-15)+28]-49

3(18-15x)+16x-36=2(6x+13)-49⇒54 - 45x +16x -36 = 12x +26 -49

-29x+18 = 12x - 23⇒18+23=12x + 29x⇒41=41x⇒ x = 1

d)

2[3(x+1)-4((2x-3)]-18=11-3[2(3x-5)-3(x+4)]

2[(3x+3)-8x+12]-18=11-3[(6x-10)-3x-12]

2[(-5x+15)]-18=11-3(6x-10-3x-12)⇒-10x+30 -18= 11 -3(3x-22)

-10x +12=11-9x+66⇒12-77=-9x+10x⇒x= -65

e)

25-4[6(x+1)-3(3x+4)]=5[2(3x-7)-3(x-5)]+23

25 - 4(6x+6-9x+12)=5(6x-14-3x+15)+23

25 - 4(15x+18)=5(3x+1)+23⇒25- 60x+-72=15x+5+23

-47-60x=15x+28⇒-47-28=15x+60x⇒-75=75x

x = -1