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