Discussion
If \(\frac{21x - 6}{4} - 9 \le 0\) and \(\frac{x - 1}{3} + 1 \ge 0, x \in \mathbb{R}\) , then \(x\) lies in the interval
Answer: B
x lies in [-2, 2].
Solve each inequality and take the common part.
\[ \begin{aligned} \frac{21x - 6}{4} \le 9 &\Rightarrow 21x \le 42 \Rightarrow x \le 2 \\ \frac{x - 1}{3} \ge -1 &\Rightarrow x - 1 \ge -3 \Rightarrow x \ge -2 \end{aligned} \]
Both conditions hold for \(-2 \le x \le 2\). Both ends are included because the inequalities are not strict. [-2, 4] and [-2, 1] come from slips in clearing the fractions.
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