Question:
$\frac{2 x+3}{5}-2<\frac{3(x-2)}{5}$
Solution:
$\frac{2 x+3}{5}-2<\frac{3(x-2)}{5}$
$\Rightarrow \frac{2 x+3}{5}-\frac{3 x-6}{5}<2 \quad\left[\right.$ Transposing $\frac{3(x-2)}{5}$ to the LHS and $-2$ to the RHS $]$
$\Rightarrow \frac{2 \mathrm{x}+3-3 \mathrm{x}+6}{5}<2$
$\Rightarrow 2 x+3-3 x+6<10 \quad$ [Multiplying both the sides by 5 ]
$\Rightarrow-\mathrm{x}+9<10$
$\Rightarrow-\mathrm{x}<1$
$\Rightarrow x>-1$ [Multiplying both the sides by $-1]$
Hence, the solution set of the given inequation is $(-1, \infty)$.
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