Discussion
The set of all x satisfying the inequalities \(-4 \leq 2 - 3x \lt 7\) is
Answer: D
The solution set is \(\left(\frac{-5}{3}, 2\right]\).
Subtract 2 throughout, then divide by -3, which reverses both inequality signs:
\[ \begin{aligned} -4 \leq 2 - 3x &\lt 7 \\ -6 \leq -3x &\lt 5 \\ 2 \geq x &\gt -\tfrac{5}{3} \end{aligned} \]
So \(x\) runs from \(-\frac{5}{3}\) (excluded) to 2 (included). Intervals such as \(\left(2, \frac{5}{3}\right)\) come from forgetting to reverse the signs, which produces an empty, back-to-front interval; the -11/3 and -7/3 endpoints come from arithmetic slips.
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