\(1)\dfrac{1}{3}x+\dfrac{2}{5}\left(x+1\right)=0\\ < =>\dfrac{1}{3}x+\dfrac{2}{5}x+\dfrac{2}{5}=0\\ < =>\dfrac{11}{15}x=\dfrac{-2}{5}\\ < =>x=\dfrac{-2}{5}:\dfrac{11}{15}\\ < =>x=\dfrac{-2}{5}\cdot\dfrac{15}{11}=\dfrac{-6}{11}\\ 2)4x-\left(2x+1\right)=3-\dfrac{1}{3}+x\\ < =>4x-2x-1=3-\dfrac{1}{3}+x\\ < =>2x-1-x=\dfrac{8}{3}\\ < =>x-1=\dfrac{8}{3}\\ < =>x=\dfrac{8}{3}+1\\ < =>x=\dfrac{11}{3}\)
\(5)3\left(x+\dfrac{1}{2}\right)-\dfrac{1}{2}\left(4x-\dfrac{2}{3}\right)=\dfrac{5}{6}\\ < =>3x+\dfrac{3}{2}-2x+\dfrac{1}{3}=\dfrac{5}{6}\\ < =>x+\dfrac{11}{6}=\dfrac{5}{6}\\ < =>x=\dfrac{5}{6}-\dfrac{11}{6}\\ < =>x=\dfrac{-6}{6}=-1\\ 7)\dfrac{11}{15}-\left(\dfrac{7}{9}+x\right)\cdot\dfrac{3}{8}=\dfrac{61}{90}+\dfrac{x}{3}\\ < =>\dfrac{11}{15}-\dfrac{7}{24}-\dfrac{3}{8}x=\dfrac{61}{90}+\dfrac{1}{3}x\\ < =>\dfrac{1}{3}x+\dfrac{3}{8}x=\dfrac{11}{15}-\dfrac{7}{24}-\dfrac{61}{90}\\ < =>\dfrac{17}{24}x=-\dfrac{17}{72}\\ < =>x=\dfrac{-17}{72}:\dfrac{17}{24}\\ < =>x=-\dfrac{1}{3}\)
