Question

2x-1/6 = 2(x-3)/3 + 1?

Answer 1

$2x-\frac{1}{6}=\frac{2(x-3)}{3}+1\ \ \ \ |multiply\ both\ sides\ by\ 6\\\\6(2x)-6(\frac{1}{6})=6\left(\frac{2x-6}{3}\right)+6(1)\\\\12x-1=2(2x-6)+6\\\\12x-1=2(2x)+2(-6)+6\\\\12x-1=4x-12+6\\\\12x-1=4x-6\ \ \ \ |add\ 1\ to\ both\ sides\\\\12x=4x-5\ \ \ \ \ |subtract\ 4x\ from\ both\ sides\\\\8x=-5\ \ \ \ |divide\ both\ sides\ by\ 8\\\\\boxed{\boxed{x=-\frac{5}{8}}}$

Answer 2

2x - 1 = 2(x-3)
   6        3 + 1
2x - 1 = 2x - 6
   6            4
4(2x - 1) = 6(2x-6)
8x - 8 = 12x - 36
-8x        -8x       
     -8 = 4x - 36
  +36         +36
    28 = 4x
    28 = 4x
     4      4
     7 = x