Question

\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\] 

Answer 1

\[\frac{3x - 2}{5} \leq \frac{4x - 3}{2}\]
\[ \Rightarrow 2\left( 3x - 2 \right) \leq 5\left( 4x - 3 \right)$$\]
\[ \Rightarrow 6x - 4 \leq 20x - 15\]
\[ \Rightarrow - 4 + 15 \leq 20x - 6x (\text{ Transposing 6x to the RHS and - 15 to the LHS })\]
\[ \Rightarrow 11 \leq 14x \]
\[ \Rightarrow 14x \geq 11\]
\[ \Rightarrow x \geq \frac{11}{14} (\text{ Dividing both the sides by 14 })\]
\[\text{ Hence, the solution set of the given inequation is } [\frac{11}{14}, \infty ) .\]