To solve this equation, we can start by simplifying both sides.

First, let's simplify the left side of the equation:

((4x-3)/5) + 1
= (4x-3)/5 + 1
= (4x-3)/5 + 5/5
= (4x-3 + 5)/5
= (4x + 2)/5

Now, let's simplify the right side of the equation:

(7-x)/3

Now, let's set the two simplified expressions equal to each other:

(4x + 2)/5 = (7-x)/3

Now, we can cross multiply to eliminate the fractions:

3(4x + 2) = 5(7-x)
12x + 6 = 35 - 5x

Now, let's solve for x:

12x + 6 = 35 - 5x
12x + 5x = 35 - 6
17x = 29
x = 29/17

Therefore, the solution to the equation is x = 29/17.