Solve the following


$\frac{x}{5}<\frac{3 x-2}{4}-\frac{5 x-3}{5}$


$\frac{x}{5}<\frac{3 x-2}{4}-\frac{5 x-3}{5}$

$\Rightarrow 20 \times\left(\frac{x}{5}\right)<20 \times\left(\frac{3 x-2}{4}-\frac{5 x-3}{5}\right) \quad$ (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 $\left(-\infty, \frac{2}{9}\right)$.

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