Question

Rezovalti ecuatiile:

a) x/2 - x/3 = 7/6
b) 2/3 + x+1/2 = 5- 4-x/6 
c) 1/4 · {1/4 · [ 1/4· (1/4 · x + 1) + 4] +1} +4 =5
d) 0,(6)x +2x - 0,(3) = 4- 2(x+1) + 3,(6)
e)12 intregi 1/3 : {[2 intregi 3/4 : (1 intreg 2/3 + 1 intreg 7/8 · x)] · 8/11 + 1 intreg 2/3 } =5

Answer 1

a)   3x -2x =7    x=7   (s-au înmulțit ambii membrii ai ecuației cu 6)

b)   4 + 3x + 3 = 30 - 4 +x            3x - x = 19       2x = 19        x = 19/2

c)   1/4·{ 1/4·[1/4·(1/4·x + 1) +4] +1} = 5 - 4 = 1

1/4·[1/4·(1/4·x +1) + 4] +1 = 1÷1/4 = 1·4/1 = 4

1/4·[1/4·(1/4·x + 1) +4] = 4 -1 = 3

1/4·(1/4·x +1) + 4 = 3 ÷1/4 = 3·4/1 = 12

1/4·(1/4·x + 1) = 12 - 4 = 8       1/4·x + 1 = 8 ÷1/4 = 8·4/1 = 32

1/4·x = 32 -1 =31       x = 31 ÷1/4 = 31·4/1 = 124

d)   [ 2/3·x + 2x - 1/3 = 4-2x - 2 +11/3  ]×3  ⇒ 2x + 6x - 1 = 6- 6x + 11   2x +6x +6x =12 ⇒  14x = 12   x =12/14 = 6/7    s-ar putea ca eu sa nu fi inteles  corect textul; verifica, dar mersul rezolvarii nu se va scimba

e)    37/3÷{[11/4 ÷(5/3 + 15/8·x )]·8/11 + 5/3} =5

[11/4÷(5/3 + 15/8·x)]·8/11 + 5/3 = 5/1×3/37 = 15/37

[11/4÷(5/3 + 15/8·x)]·8/11 = 15/37 - 5/3 = - 140/111

11/4÷(5/3 + 15/8·x) = -140/111·11/8 = - 385/222·

5/3 + 15/8·x  = -385/222× 4/11 = - 35·2/111 = -70/111

15/8·x = -70/111 - 5/3 = - 255/111     x= -255/111×8/15 =-136/111   VERIFICA !!!!1