Given:
\(\frac{{\text{x}}}{4} < \frac{(5{\text{x}}-2)}{3} - \frac{(7{\text{x}}-3)}{5}\), where x ϵ R.
Multiplying 60 on both the sides in the above equation,
\(\frac{{\text{x}}}{4}(60) < \frac{(5{\text{x}}-2)}{3}(60) - \frac{(7{\text{x}}-3)}{5}(60)\)
15x < 20(5x - 2) – 12(7x - 3)
15x < 100x – 40 – 84x + 36
15x < 16x – 4
Now, subtracting 16x from both sides in above equation
15x – 16x < 16x – 4 – 16x
-x < -4
Now, multiplying by -1 on both sides in above equation
(-x)(-1) < (-4)(-1)
x > 4 (inequality sign reversed)