To solve the equation 3x - 5/3 = x - 1/4, we can start by getting rid of the fractions.

First, let's multiply every term in the equation by 12 to eliminate the denominators:

12 * (3x - 5/3) = 12 * (x - 1/4)

This simplifies to:

12 * 3x - 12 * (5/3) = 12 * x - 12 * (1/4)

36x - 20 = 12x - 3

Next, let's combine like terms:

36x - 20 = 12x - 3

Subtract 12x from both sides:

36x - 12x - 20 = 12x - 12x - 3

24x - 20 = -3

Add 20 to both sides:

24x - 20 + 20 = -3 + 20

24x = 17

Finally, divide both sides by 24 to solve for x:

24x/24 = 17/24

x = 17/24