a) \(\dfrac{4}{3}-\dfrac{1}{3}\):\(\left(x-\dfrac{1}{2}\right)=\dfrac{5}{6}\)
\(\dfrac{1}{3}\):\(\left(x-\dfrac{1}{2}\right)=\dfrac{4}{3}-\dfrac{5}{6}\)
\(\dfrac{1}{3}\):\(\left(x-\dfrac{1}{2}\right)=\dfrac{8}{6}-\dfrac{5}{6}\)
\(\dfrac{1}{3}\):\(\left(x-\dfrac{1}{2}\right)=\dfrac{1}{2}\)
\(x-\dfrac{1}{2}=\dfrac{1}{3}\):\(\dfrac{1}{2}\)
\(x-\dfrac{1}{2}=\dfrac{1}{3}.2\)
\(x-\dfrac{1}{2}=\dfrac{2}{3}\)
\(x=\dfrac{2}{3}+\dfrac{1}{2}\)
\(x=\dfrac{4}{6}+\dfrac{3}{6}\)
\(x=\dfrac{7}{6}\)
b) \(x-\dfrac{4}{9}=\dfrac{2}{3}x\)
\(\dfrac{4}{9}=x-\dfrac{2}{3}x\)
\(\dfrac{4}{9}=x\left(1-\dfrac{2}{3}\right)\)
\(\dfrac{4}{9}=\dfrac{1}{3}x\)
\(x=\dfrac{4}{9}\):\(\dfrac{1}{3}\)
\(x=\dfrac{4}{9}.3\)
\(x=\dfrac{4}{3}\)
c) \(\dfrac{3}{4}-\dfrac{1}{4}x=\dfrac{1}{2}x-\dfrac{3}{8}\)
\(\dfrac{3}{4}+\dfrac{3}{8}=\dfrac{1}{2}x+\dfrac{1}{4}x\)
\(\dfrac{9}{8}=\dfrac{3}{4}x\)
\(x=\dfrac{3}{2}\)