a) \(\dfrac{1}{5}+x=-\dfrac{1}{2}\)
\(x=-\dfrac{1}{2}-\dfrac{1}{5}=-\dfrac{7}{10}\)
b) \(1\dfrac{3}{4}x+1\dfrac{1}{2}=-\dfrac{4}{5}\)
\(\dfrac{7}{4}x+\dfrac{3}{2}=-\dfrac{4}{5}\)
\(\dfrac{7}{4}x=-\dfrac{4}{5}-\dfrac{3}{2}=-\dfrac{23}{10}\)
\(x=\dfrac{-47}{35}\)
c) \(\left|x+\dfrac{3}{4}\right|-5=-2\)
\(\left|x+\dfrac{3}{4}\right|=-2+5=3\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{3}{4}=3\\x+\dfrac{3}{4}=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{9}{4}\\x=-\dfrac{15}{4}\end{matrix}\right.\)
d) \(-\dfrac{5}{8}+x=\dfrac{4}{9}\)
\(x=\dfrac{4}{9}+\dfrac{5}{8}\)
\(x=\dfrac{77}{72}\)