a: \(-4\left(x-\dfrac{1}{3}\right)=-\dfrac{8}{3}\)
=>\(x-\dfrac{1}{3}=\dfrac{-8}{3}:\left(-4\right)=\dfrac{2}{3}\)
=>\(x=\dfrac{2}{3}+\dfrac{1}{3}=1\)
b: \(\dfrac{x-1}{2}=\dfrac{2-x}{3}\)
=>3(x-1)=2(2-x)
=>3x-3=4-2x
=>5x=7
=>\(x=\dfrac{7}{5}\)
c: \(\dfrac{5}{4}-\dfrac{1}{4}:x=\dfrac{2}{3}\)
=>\(\dfrac{1}{4}:x=\dfrac{5}{4}-\dfrac{2}{3}=\dfrac{7}{12}\)
=>\(x=\dfrac{1}{4}:\dfrac{7}{12}=\dfrac{1}{4}\cdot\dfrac{12}{7}=\dfrac{3}{7}\)
d: \(\dfrac{2}{5}\left(\dfrac{1}{2}-\dfrac{1}{2}x\right)-\dfrac{3}{5}\left(\dfrac{1}{3}x+\dfrac{10}{3}\right)=-\dfrac{1}{4}\)
=>\(\dfrac{1}{5}-\dfrac{1}{5}x-\dfrac{1}{5}x-2=-\dfrac{1}{4}\)
=>\(-\dfrac{2}{5}x-\dfrac{9}{5}=-\dfrac{1}{4}\)
=>\(-\dfrac{2}{5}x=-\dfrac{1}{4}+\dfrac{9}{5}=\dfrac{31}{20}\)
=>\(x=-\dfrac{31}{20}:\dfrac{2}{5}=-\dfrac{31}{20}\cdot\dfrac{5}{2}=\dfrac{-31}{8}\)
