A. \(2 \frac{2}{3}<x \leq-2\) B. \(-2 \leq x\) \(<2 \frac{2}{3}\) C. \(x \geq-2, x 2 \frac{2}{3}\) D. \(x \leq-2, x<2 \frac{2}{3}\)
Correct Answer: B
Explanation
The inequality \(-3<5-3 x \leq 11\) can be split into (i) \(-3<5-3 x \&\) (ii) \(5-3 x \leq 11\)rom (i), \begin{array}{l} 3 x<5+3 \\ 3 x<8 \\ x<\frac{8}{3} \\ x<2 \frac{2}{3} \\ \text { From (ii) } \\ -3 x \leq 11-5 \\ -3 x \leq 6 \end{array} \begin{array}{l} x \geq \frac{6}{-3} \\ x \geq-2 \\ -2 \leq x \end{array} The combined solution is: \(-2 \leq x<2 \frac{2}{3}\)