To solve the equation, we need to combine like terms and isolate the variable.

Starting with the left side of the equation:
3x + 2/2 - 3x + 1/6

The term 2/2 simplifies to 1, so we have:
3x + 1 - 3x + 1/6

Combining like terms:
(3x - 3x) + 1 + 1/6

The 3x and -3x cancel each other out, leaving us with:
1 + 1/6

To add these fractions, we need a common denominator, which is 6. So we have:
6/6 + 1/6 = 7/6

Now, let's simplify the right side of the equation:
5/3 + 2

To add these fractions, we need a common denominator, which is 3. So we have:
5/3 + 6/3 = 11/3

Now, our equation becomes:
7/6 = 11/3

To solve for x, we need to get rid of the fractions. We can do this by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 6:
6 * (7/6) = 6 * (11/3)

On the left side, the 6 in the numerator cancels out with the 6 in the denominator, leaving us with:
7

On the right side, we have:
6 * (11/3) = 66/3 = 22

So our equation becomes:
7 = 22

Since 7 is not equal to 22, there is no solution to this equation.