Question

Rezolvați ecuațiile:
a) 2/3+x+1/2=5/1-4-x/6
b) 6x/5-x/1=x/3+8x/1
c) 1/4•{1/4•[1/4•(1/4•x+1)+4]+1}+4=5 (eu trebuie să demomstrez că e = cu 5)
d) 0,(6)x+2x-0,(3)=4-2(x+1)+3,(6)
e) 37/3:{[11/4:(5/3+15/8•x)]•8/11+5/3}=5 (eu trebuie să demonstrez că e egal cu 5)

Answer 1

 2/3 + (x+1)/2=5/1-(4-x)/6
4+3x+3=30-4+x
2x=19
x=19/2

 6x/5 -x/1=x/3+8x
18x-15x=5x+120x
122x=0
x=0

1/4*{1/4*[1/4*(1/4*x+1)+4]+1}+4=5
1/4*{1/4*[1/4*(1/4*x+1)+4]+1}=5-4
1/4*{1/4*[1/4*(1/4*x+1)+4]+1}=1
{1/4*[1/4*(1/4*x+1)+4]+1}=4 
1/4*[1/4*(1/4*x+1)+4]=4-1 
1/4*[1/4*(1/4*x+1)+4]=3
1/4*(1/4*x+1)+4=12
1/4*(1/4*x+1)=8
1/4*x+1=32
1/4*x=31
x=124


 0,(6)x+2-0,(3)=4-2(x+1)+ 3,(6)
0,(6)=6/9=2/3
0,(3)=3/9=1/3
3,(6)=(36-3)/9=33/9=11/3
2x/3+2-1/3=4-2x-2+11/3
2x/3=2-2x-2+11/3+1/3
2x/3=-2x+4
2x=-6x+12
8x=12
x=12/8=3/2


37/3:{[11/4:(5/3+15x/8)]*8/11+5/3}=5
[11/4:(5/3+15x/8)]*8/11+5/3=37/15
11/4:(5/3+15x/8)*8/11=37/15-5/3 
11/4:(5/3+15x/8)*8/11=(37-25)/15 
11/4:(5/3+15x/8)*8/11=12/15 
11/4:(5/3+15x/8)=4/5 *11/8 
11/4:(5/3+15x/8)=11/10
5/3+15x/8=5/2 
15x/8=5/2 -5/3
15x/8=(15-10)/6
15x/8=5/6
x=4/9