To solve for x, we need to isolate the variable on one side of the equation.

First, we can simplify the fractions by finding a common denominator. The least common multiple of 6 and 3 is 6, and the least common multiple of 2 and 3 is 6 as well.

-5/6 + 3x = 2/3 - 1/2x

Multiplying both sides by 6 to clear the denominators:

-5 + 18x = 4 - 3x

Next, we can add 3x to both sides to get all the x terms on one side:

-5 + 21x = 4

Then, we can add 5 to both sides to isolate the x term:

21x = 9

Finally, we can divide both sides by 21 to solve for x:

x = 9/21

Simplifying the fraction:

x = 3/7

Therefore, the solution to the equation is x = 3/7.