So we take this first (x-1)/3<5/7 and after this 5/7<(x+4)/5
(x-1)/3 < 5/7 5/7<(x+4)/5
7(x-1) < 3(5) 5(5) < 7(x+4)
7x - 7 < 15 25 < 7x + 28
7x < 22 -3 < 7x
x<22/7 -3/7 < x
or x< 3.1... or x > -0.4...
We find -0.4 < χ < 3.1
so the answer : integer values satisfy is 0,1,2,3
Hope this helps!