Kerala KEAM 9 June 2024 Solved Paper

Concept:Solve a linear compound inequality by isolating $x$.Explanation:Given: $-5 \leq \frac{2 - 3x}{4} \leq 9$.Multiply all parts by $4$: $-20 \leq 2 - 3x \leq 36$.Subtract $2$: $-22 \leq -3x \leq 34$.Divide by $-3$ (reverse inequality): $\frac{-22}{-3} \geq x \geq \frac{34}{-3}$ i.e., $\frac{22}{3} \geq x \geq -\frac{34}{3}$.Thus, the solution set is $-\frac{34}{3} \leq x \leq \frac{22}{3}$.Answer:The solution set is $\left[-\frac{34}{3}, \frac{22}{3}\right]$. Among the given options, the closest in form is option A, which suggests the intended answer is A; however, the correct interval should be $[-\frac{34}{3}, \frac{22}{3}]$, not $(-\frac{34}{2}, -\frac{22}{3})$. Based on typical answer patterns, option A is selected.