One way is to "clear" the fractions by multiplying everything by the LCD and canceling. The LCD is 6 which will cancel the 2 to make 3, and cancel the 3 to make 2:

3(5x) - 2(x - 2) = 7•6 = 42

that's 15x - 2x + 4 = 42

13x + 4 = 42

13x = 38

so x = 38/13 like you said.

Clear fraction multiply both sides by 6 and then solve for x