Đáp án đúng: A
Giải chi tiết:\(\begin{array}{l}\,\,\left| {x + 1} \right| + \frac{2}{5} = 1\frac{3}{4}:\frac{5}{4} + 2\,\\\,\,\,\,\,\,\,\left| {x + 1} \right| + \frac{2}{5} = \frac{7}{4}:\frac{5}{4} + 2\,\\\,\,\,\,\,\,\left| {x + 1} \right| + \frac{2}{5} = \frac{7}{4} \cdot \frac{4}{5} + 2\\\,\,\,\,\,\,\left| {x + 1} \right| + \frac{2}{5} = \frac{7}{5} + 2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\\\,\,\,\,\,\,\left| {x + 1} \right| = \frac{7}{5} + 2\, - \frac{2}{5}\\\,\,\,\,\,\,\left| {x + 1} \right| = 3\\\,\,\,\, \Rightarrow \left[ \begin{array}{l}x + 1 = 3\\x + 1 = - 3\end{array} \right.\,\,\,\, \Rightarrow \left[ \begin{array}{l}x = 3 - 1\\x = - 3 - 1\end{array} \right. \Rightarrow \left[ \begin{array}{l}x = 2\\x = - 4\end{array} \right.\end{array}\)
Vậy \(x = 2\) hoặc \(x = - 4\).
Chọn A.