find the region which satisfy the inequalities(2x/5-3y/8<12y/13)?

Answer 1

IF your ONE inequality is: (2x/5) - (3y/8) < (12y/13)

multiplying thru by [(5)(8)(13)] and simplifying I get

(208/675)x < y

so your region of solutions {(x,y) | y > (208)x / (675)} is all points above the line y = (208)x / (675).

This line is one passing thru the origin (0,0) and has a slope =
208/675. Points of the line are NOT in your solution region.

Answer 2

I think better in decimal:

0.4X-.375Y < 0.923Y

or

Y > .308X

Consider the line Y = .308X, then the original inequality is satisfied for the region above, but not including this line