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Question
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
Solution
\[\frac{5 - 2x}{3} < \frac{x}{6} - 5\]
\[ \Rightarrow \frac{5 - 2x}{3} - \frac{x}{6} < - 5 \left[ \text{ Transposing } \frac{x}{6}to the LHS \right]\]
\[ \Rightarrow \frac{2\left( 5 - 2x \right) - x}{6} < - 5 \]
\[ \Rightarrow \frac{10 - 4x - x}{6} < - 5 \]
\[ \Rightarrow \frac{10 - 5x}{6} < - 5 \]
\[ \Rightarrow 10 - 5x < - 30\]
\[ \Rightarrow 10 + 30 < 5x\]
\[ \Rightarrow 40 < 5x\]
\[ \Rightarrow 5x > 40\]
\[ \Rightarrow x > \frac{40}{5}\]
\[ \Rightarrow x > 8\]
\[\text{ Hence, the solution set of the given inequality is } \left( 8, \infty \right) .\]
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