Question

\[2\left( 3 - x \right) \geq \frac{x}{5} + 4\]

Answer 1

\[2\left( 3 - x \right) \geq \frac{x}{5} + 4\]
\[ \Rightarrow 6 - 2x \geq \frac{x}{5} + 4\]
\[ \Rightarrow 6 - 4 \geq \frac{x}{5} + 2x \left[ \text{ Transposing - 2x to the RHS and 4 to the LHS } \right]\]
\[ \Rightarrow 2 \geq \frac{11x}{5}\]
\[ \Rightarrow \frac{11x}{5} \leq 2\]
\[ \Rightarrow x \leq \frac{10}{11} \left[ \text{ Mltiplying both the sides by } \frac{5}{11} \right]\]
\[\text{ Thus, the solution set of the given inequation is } ( - \infty , \frac{10}{11}] .\]