a)\(\left(5,75\right):x=\dfrac{14}{23}\)
\(\Rightarrow\dfrac{23}{4}:x=\dfrac{14}{23}\)
\(\Rightarrow x=\dfrac{529}{56}\)
b)\(\left(\dfrac{2x}{5}-1\right)\left(-5\right)=\dfrac{1}{4}\)
\(\Rightarrow\dfrac{2x}{5}-1=\dfrac{-1}{20}\)
\(\Rightarrow\dfrac{2x}{5}=\dfrac{19}{20}\)
\(\Rightarrow2x=\dfrac{19}{4}\)
\(\Rightarrow x=\dfrac{19}{8}\)
c)\(\dfrac{x-5}{12,1}=\dfrac{10}{x-5}\)
\(\Rightarrow\left(x-5\right)\left(x-5\right)=10.12,1\)
\(\Rightarrow\left(x-5\right)^2=121\)
\(\Rightarrow\left[{}\begin{matrix}x-5=11\\x-5=-11\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=16\\x=-6\end{matrix}\right.\)
d)
\(2\dfrac{1}{4}x-9\dfrac{1}{4}=20\)
\(\Rightarrow\dfrac{9}{4}x-\dfrac{37}{4}=20\)
\(\Rightarrow\dfrac{9}{4}x=\dfrac{117}{4}\)
\(\Rightarrow x=13\)
