To solve the inequality 2x + 1/3 - 3x - 2/2 > 1/6, we need to simplify and isolate the variable x.

First, let's simplify the expression on the left side of the inequality:

2x + 1/3 - 3x - 2/2 > 1/6

Combine like terms:

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

-x + 1/3 - 1 > 1/6

Now, let's find a common denominator for the fractions:

-x + 2/6 - 6/6 > 1/6

Combine the fractions:

(-x + 2 - 6)/6 > 1/6

Simplify:

(-x - 4)/6 > 1/6

Now, let's multiply both sides of the inequality by 6 to eliminate the fraction:

6 * (-x - 4)/6 > 6 * 1/6

Simplify:

-x - 4 > 1

Add 4 to both sides of the inequality:

-x - 4 + 4 > 1 + 4

Simplify:

-x > 5

Multiply both sides of the inequality by -1 (and reverse the inequality sign since we are multiplying by a negative number):

x < -5

Therefore, the solution to the inequality 2x + 1/3 - 3x - 2/2 > 1/6 is x < -5.