Đáp án đúng: C
Giải chi tiết:\(\begin{array}{l}\,4 - \left| {x + \frac{2}{3}} \right| = - 1\\ \Leftrightarrow 4 + 1 = \left| {x + \frac{2}{3}} \right|\\ \Leftrightarrow \left| {x + \frac{2}{3}} \right| = 5\,\,\,\,\,\,\left( * \right)\end{array}\)
TH1: \(x + \frac{2}{3} \ge 0 \Leftrightarrow x \ge \frac{{ - 2}}{3}\)
Khi đó:
\(\begin{array}{l}\left( * \right) \Leftrightarrow x + \frac{2}{3} = 5\\\,\,\,\,\,\,\, \Leftrightarrow x\,\,\,\,\,\,\,\,\, = 5 - \frac{2}{3}\\\,\,\,\,\,\,\, \Leftrightarrow x\,\,\,\,\,\,\,\,\, = \frac{{13}}{3}\,\,\,\,\,\,\left( {TM} \right)\end{array}\)
TH2: \(x + \frac{2}{3} < 0 \Leftrightarrow x < \frac{{ - 2}}{3}\)
Khi đó:
\(\begin{array}{l}\left( * \right) \Leftrightarrow x + \frac{2}{3} = - 5\\\,\,\,\,\,\,\, \Leftrightarrow \,x\,\,\,\,\,\,\,\,\,\, = - 5 - \frac{2}{3}\\\,\,\,\,\,\, \Leftrightarrow x\,\,\,\,\,\,\,\,\,\, = \frac{{ - 17}}{3}\,\,\,\,\,\left( {TM} \right)\end{array}\)
Vậy \(x = \frac{{13}}{3}\) hoặc \(x = \frac{{ - 17}}{3}\)
Chọn C
