Question

Sa se rezolve ecuatia : 0,(1x)+0,(2x)+0,(3x)+...+0,(9x)=x

Answer 1

a) 0,(1x)+0,(2x)+...+0,(9x)=x

1x/99+2x/99+...9x/99=x
(10+x)/99+(20+x)/99+...(90+x/99)=x
10/99+x/99+20/99+x/99+...+90/99+x/99=x
9*x/99+(10+20+30+...90)/99=x
9*x/99+450/99=x
9x+450=99x
90x=450
x=5

b)0,(6)x +2x-0,(3)=4-2(x+1)+3,(6)
    x*6/9+2x -3/9 =4 -2*x-2+ (36-3)/9
2x/3+2x-1/3=2-2x+33/9
2x/3+2x-1/3=2-2x+11/3
2x/3+4x=6/3+11/3+1/3
2x/3+12x/3=18/3
14x=18/3*3=18
x=18/14=9/7