Discussion
The set of all x satisfying the inequality \(|3 - 4x| \le 11\) is
Answer: B
The solution set is \(\left[-2, \frac{7}{2}\right]\).
\(|u| \le 11\) means \(-11 \le u \le 11\):
\[ \begin{aligned} -11 \le 3 - 4x &\le 11 \\ -14 \le -4x &\le 8 \\ -2 \le x &\le \tfrac{7}{2} \end{aligned} \]
Dividing by \(-4\) reverses both inequalities. Check: \(x = -2\) gives \(|11| = 11\) and \(x = 3.5\) gives \(|-11| = 11\). \([-2, 7]\) forgets to divide 14 by 4, and the other intervals have the signs reversed.
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