Đáp án đúng: A
Giải chi tiết:\(\begin{array}{l}0,5 + \left| {x + \frac{1}{2}} \right| = \left| {\frac{{ - 3}}{{\sqrt {16} }}} \right|\\\,\,\,\frac{1}{2} + \left| {x + \frac{1}{2}} \right| = \left| {\frac{{ - 3}}{4}} \right|\\\,\,\,\frac{1}{2} + \left| {x + \frac{1}{2}} \right| = \frac{3}{4}\\\,\,\,\,\,\,\,\,\,\,\,\left| {x + \frac{1}{2}} \right| = \frac{3}{4} - \frac{1}{2}\\\,\,\,\,\,\,\,\,\,\,\,\left| {x + \frac{1}{2}} \right| = \frac{1}{4}\end{array}\)
\( \Rightarrow x + \frac{1}{2} = \frac{1}{4}\)hoặc \(x + \frac{1}{2} = \frac{{ - 1}}{4}\)
\( \Rightarrow x = \frac{1}{4} - \frac{1}{2}\) hoặc \(x = \frac{{ - 1}}{4} - \frac{1}{2}\)
\( \Rightarrow x = \frac{{ - 1}}{4}\) hoặc \(x = \frac{{ - 3}}{4}\)
Vậy \(x = \frac{{ - 1}}{4}\) hoặc \(x = \frac{{ - 3}}{4}\)
Chọn A