Giá trị biểu thức \(\dfrac{{31}}{4}:\left[ {\dfrac{1}{7} - \left( {\dfrac{3}{4} + \dfrac{1}{2}} \right)} \right] + 0,5\) bằng:

\(\begin{array}{l}\dfrac{{31}}{4}:\left[ {\dfrac{1}{7} - \left( {\dfrac{3}{4} + \dfrac{1}{2}} \right)} \right] + 0,5\\ = \dfrac{{31}}{4}:\left[ {\dfrac{1}{7} - \left( {\dfrac{3}{4} + \dfrac{2}{4}} \right)} \right] + \dfrac{1}{2}\\ = \dfrac{{31}}{4}:\left( {\dfrac{1}{7} - \dfrac{5}{4}} \right) + \dfrac{1}{2}\\ = \dfrac{{31}}{4}:\left( {\dfrac{4}{{28}} - \dfrac{{35}}{{28}}} \right) + \dfrac{1}{2}\\ = \dfrac{{31}}{4}:\dfrac{{( - 31)}}{{28}} + \dfrac{1}{2}\\ = \dfrac{{31}}{4}.\dfrac{{( - 28)}}{{31}} + \dfrac{1}{2}\\ = \dfrac{{ - 28}}{4} + \dfrac{1}{2}\\ = \dfrac{{ - 14}}{2} + \dfrac{1}{2}\\ = \dfrac{{ - 13}}{2}.\end{array}\)