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

1/3x-1/6=1/2x+1/3
Therefore 1/3x-1/2x = 1/2+1/6
The LCM of left hand side is 6x
So we get(2-3)/6x = (3+2)/6
Therefore x = -1/5

x/a million = 3x + a million a million/3 x= 3x + 4/3 -4/3 = 3x-x -4/3 = 2x -2/3 =x verify by ability of substitution: -2/3/2-a million = (-2/3)(3) + a million a million/3 -2/3/a million = -2 + 4/3 -2/3 = (-6+4)/3 -2/3 = -2/3 or in case you meant : x/2 - a million = 3x + a million a million/3 then x could be equivalent to -14/15 i'm hoping this helps.

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

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

1/3x-1/6=1/2x+1/3
First multiply everything by a common denominator, such as 6
6 (1/3x-1/6) = 6(1/2x+1/3)
Next distribute the 6's into your parentheses ...
6/3x - 6/6 = 6/2x + 6/3
Simplify
2x - 1 = 3x + 2
subtract 2x
-1 = x + 2
subtract 2
-3 = x

Check: 1/3(-3) - 1/6 = 1/2(-3) + 1/3
-1 - 1/6 = -3/2 + 1/3
multiply by 6 again
6( -1 - 1/6) = 6 (-3/2 + 1/3)
-6 - 1 = -18/2 + 6/3
-7 = -9 + 2
-7 = -7
checks out, the answer is correct!
x = -3