To solve this equation, we first need to simplify the left side of the equation by finding a common denominator.

(5x-1)/4 - (x-3)/3
= (3(5x-1) - 4(x-3))/12
= (15x - 3 - 4x + 12)/12
= (11x + 9)/12

Now, we can rewrite the equation with the simplified left side:

(11x + 9)/12 = 10 - x

To get rid of the fraction, we can multiply both sides by 12:
11x + 9 = 120 - 12x

Next, we can simplify by adding 12x to both sides:
23x + 9 = 120

Subtract 9 from both sides:
23x = 111

Finally, divide by 23 to solve for x:
x = 111/23
x = 4.827

Therefore, the solution to the equation is x = 4.827.