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