Question:
$\frac{x}{5}<\frac{3 x-2}{4}-\frac{5 x-3}{5}$
Solution:
$\frac{x}{5}<\frac{3 x-2}{4}-\frac{5 x-3}{5}$
$\Rightarrow 20 \times\left(\frac{x}{5}\right)<20 \times\left(\frac{3 x-2}{4}-\frac{5 x-3}{5}\right) \quad$ (Multiplying both the sides by 20$)$
$\Rightarrow 4 x<5(3 x-2)-4(5 x-3)$
$\Rightarrow 4 x<15 x-10-20 x+12$
$\Rightarrow 4 x<-5 x+2$
$\Rightarrow 4 x+5 x<2 \quad$ (Transposing $-5 x$ to the LHS)
$\Rightarrow 9 \mathrm{x}<2$
$\Rightarrow x<\frac{2}{9} \quad$ (Dividing both the sides by 9 )
Hence, the solution set of the given inequation is $\left(-\infty, \frac{2}{9}\right)$.