To solve for x, first we need to get rid of the fractions by multiplying every term by the least common multiple of the denominators, which is 24.

(24)(1/6x) - (24)0.82 = (24)(3/8x) - (24)1.37
4x - 19.68 = 9x - 32.88

Next, we want to isolate the x terms on one side of the equation. Let's subtract 4x from both sides:

-19.68 = 5x - 32.88

Now, let's add 32.88 to both sides:

32.88 - 19.68 = 5x
13.2 = 5x

Finally, divide by 5 to solve for x:

x = 13.2 / 5
x = 2.64

Therefore, the solution to the equation is x = 2.64.