Given,
(7x-5)/(8x+3) > 4
For this inequation to be true,
There are two possible cases.
i. 25x + 17 > 0 and 8x + 3 < 0
⇒ 25x + 17 – 17 > 0 – 17 and
8x + 3 – 3 < 0 – 3
⇒ 25x > –17 and 8x < –3
ii. 25x + 17 < 0 and 8x + 3 > 0
⇒ 25x + 17 – 17 < 0 – 17 and
8x + 3 – 3 > 0 – 3
⇒ 25x < –17 and 8x > –3
Hence,
This case is not possible.
Thus,
The solution of the given inequation is (\(-\frac{17}{25}\),\(-\frac{3}{8}\)).
