To solve this inequality, we need to simplify it first.

3x + 5/7 + 10 - 3x/5 > 2x + 7/3

First, let's simplify the terms:

(3x - 3x/5) + (5/7 + 10) > 2x + 7/3

Now, simplify further:

(15x/5 - 3x/5) + (35/7 + 70/7) > 6x + 21/3

(12x/5) + (105/7) > 6x + 7

(12x/5) + (15x) > 6x + 7

(12x + 75x)/5 > 6x + 7

87x/5 > 6x + 7

Multiply through by 5 to clear the denominator:

87x > 30x + 35

Subtract 30x from both sides:

57x > 35

Divide by 57 to isolate x:

x > 35/57

Therefore, the solution to the inequality is x > 35/57.