Question

\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]

Answer 1

\[\frac{4 + 2x}{3} \geq \frac{x}{2} - 3\]
\[ \Rightarrow \frac{4 + 2x}{3} - \frac{x}{2} \geq - 3\]
\[ \Rightarrow \frac{8 + 4x - 3x}{6} \geq - 3\]
\[ \Rightarrow 8 + x \geq - 18 \left[ \text{ Multiplying both the sides by 6 } \right]\]
\[ \Rightarrow x \geq - 26 \left[ \text{ Transposing 8 to the RHS } \right]\]
\[\text{ Thus, the solution set of the given inequation is } [ - 26, \infty ) .\]