Given,
(4x+3)/(2x-5) < 6
For this inequation to be true,
There are two possible cases.
i. 8x – 33 > 0 and 2x – 5 > 0
⇒ 8x – 33 + 33 > 0 + 33 and
2x – 5 + 5 > 0 + 5
⇒ 8x > 33 and 2x > 5
ii. 8x – 33 < 0 and 2x – 5 < 0
⇒ 8x – 33 + 33 < 0 + 33 and
2x – 5 + 5 < 0 + 5
⇒ 8x < 33 and 2x < 5
Thus,
The solution of the given inequation is (- ∞,\(\frac{5}{2}\)) ∪ (\(\frac{33}{8}\),∞).
