\(a,\dfrac{2}{3}-\dfrac{1}{3}\left(x-\dfrac{3}{2}\right)-\dfrac{1}{2}\left(2x+1\right)=5\)

\(\dfrac{2}{3}-\dfrac{1}{3}x-\dfrac{1}{2}-x+\dfrac{1}{2}=5\)

\(\dfrac{2}{3}-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}x-x=5\)

\(\dfrac{2}{3}-\dfrac{1}{3}x-x=5\)

\(\dfrac{2}{3}-\dfrac{4}{3}x=5\)

\(\dfrac{4}{3}x=\dfrac{2}{3}-5\)

\(\dfrac{4}{3}x=-\dfrac{13}{3}\)

\(x=-\dfrac{13}{3}:\dfrac{4}{3}\)

\(x=-\dfrac{13}{4}\)

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\(b,\left(x+\dfrac{1}{2}\right)\left(\dfrac{3}{4}-x\right)=0\)

\(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{1}{2}=0\\\dfrac{3}{4}-x=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{1}{2}\\x=\dfrac{3}{4}\end{matrix}\right.\)

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\(c,\dfrac{2x-1}{-3+2}=0\)

\(\Rightarrow2x-1=0\)

\(\Rightarrow x=\dfrac{1}{2}\)

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