The solution can be symbolised graphically by drawing two lines:
y=(3x-1)/5 - 2 and y=2-x/3
Where the lines cross is the solution for x. See below for this intersection.
This is where (3x-1)/5-2=2-x/3,
3(3x-1)-30=30-5x, 9x-3-30=30-5x, 14x=63, x=63/14=9/2=4.5. This is the x value (the solution) where the lines cross. y=2-4.5/3=(13.5-1)/5-2=0.5 or ½.