1: \(2x+\dfrac{1}{2}=-\dfrac{5}{3}\)
=>\(2x=-\dfrac{5}{3}-\dfrac{1}{2}=-\dfrac{10}{6}-\dfrac{3}{6}=-\dfrac{13}{6}\)
=>\(x=-\dfrac{13}{6}:2=-\dfrac{13}{12}\)
2: \(\dfrac{1}{7}-\dfrac{3}{5}x=\dfrac{3}{5}\)
=>\(\dfrac{3}{5}x=\dfrac{1}{7}-\dfrac{3}{5}=\dfrac{5}{35}-\dfrac{21}{35}=-\dfrac{16}{35}\)
=>\(x=-\dfrac{16}{35}:\dfrac{3}{5}=-\dfrac{16}{35}\cdot\dfrac{5}{3}=\dfrac{-16}{7\cdot3}=-\dfrac{16}{21}\)
3: \(-3x-\dfrac{3}{4}=\dfrac{6}{5}\)
=>\(-3x=\dfrac{3}{4}+\dfrac{6}{5}=\dfrac{15}{20}+\dfrac{24}{20}=\dfrac{39}{20}\)
=>\(x=\dfrac{39}{20}:\left(-3\right)=-\dfrac{13}{20}\)
4: \(\dfrac{3}{7}-\dfrac{1}{2}x=\dfrac{5}{3}\)
=>\(\dfrac{1}{2}x=\dfrac{3}{7}-\dfrac{5}{3}=\dfrac{9}{21}-\dfrac{35}{21}=-\dfrac{26}{21}\)
=>\(x=-\dfrac{26}{21}\cdot2=-\dfrac{52}{21}\)
5: \(2x-\dfrac{3}{4}=-\dfrac{5}{8}\)
=>\(2x=-\dfrac{5}{8}+\dfrac{3}{4}=-\dfrac{5}{8}+\dfrac{6}{8}=\dfrac{1}{8}\)
=>\(x=\dfrac{1}{8}:2=\dfrac{1}{16}\)
6: \(\dfrac{3}{5}-\dfrac{1}{4}x=\dfrac{2}{5}\)
=>\(\dfrac{1}{4}x=\dfrac{3}{5}-\dfrac{2}{5}=\dfrac{1}{5}\)
=>\(x=\dfrac{1}{5}:\dfrac{1}{4}=\dfrac{4}{5}\)
7: \(-\dfrac{2}{3}x+2=\dfrac{3}{4}\)
=>\(-\dfrac{2}{3}x=\dfrac{3}{4}-2=-\dfrac{5}{4}\)
=>\(x=\dfrac{5}{4}:\dfrac{2}{3}=\dfrac{5}{4}\cdot\dfrac{3}{2}=\dfrac{15}{8}\)
8: \(\dfrac{2}{5}x+\dfrac{3}{2}=\dfrac{5}{4}\)
=>\(\dfrac{2}{5}x=\dfrac{5}{4}-\dfrac{3}{2}=-\dfrac{1}{4}\)
=>\(x=-\dfrac{1}{4}:\dfrac{2}{5}=-\dfrac{1}{4}\cdot\dfrac{5}{2}=-\dfrac{5}{8}\)
9: \(\dfrac{3}{4}x-\dfrac{5}{2}=\dfrac{4}{3}\)
=>\(\dfrac{3}{4}x=\dfrac{5}{2}+\dfrac{4}{3}=\dfrac{15}{6}+\dfrac{8}{6}=\dfrac{23}{6}\)
=>\(x=\dfrac{23}{6}:\dfrac{3}{4}=\dfrac{23}{6}\cdot\dfrac{4}{3}=\dfrac{92}{18}=\dfrac{46}{9}\)
10: \(-2x+\dfrac{3}{14}=\dfrac{1}{7}-\dfrac{4}{21}\)
=>\(-2x+\dfrac{3}{14}=\dfrac{3}{21}-\dfrac{4}{21}=-\dfrac{1}{21}\)
=>\(-2x=-\dfrac{1}{21}-\dfrac{3}{14}=-\dfrac{2}{42}-\dfrac{9}{42}=-\dfrac{11}{42}\)
=>\(x=\dfrac{11}{84}\)
11: \(\dfrac{3}{2}x-\dfrac{1}{4}=\dfrac{2}{3}\)
=>\(\dfrac{3}{2}x=\dfrac{2}{3}+\dfrac{1}{4}=\dfrac{8}{12}+\dfrac{3}{12}=\dfrac{11}{12}\)
=>\(x=\dfrac{11}{12}:\dfrac{3}{2}=\dfrac{11}{12}\cdot\dfrac{2}{3}=\dfrac{22}{36}=\dfrac{11}{18}\)
12: \(\dfrac{2}{3}-\dfrac{4}{7}x=1-\dfrac{1}{2}\)
=>\(\dfrac{2}{3}-\dfrac{4}{7}x=\dfrac{1}{2}\)
=>\(\dfrac{4}{7}x=\dfrac{2}{3}-\dfrac{1}{2}=\dfrac{1}{6}\)
=>\(x=\dfrac{1}{6}:\dfrac{4}{7}=\dfrac{1}{6}\cdot\dfrac{7}{4}=\dfrac{7}{24}\)
13: \(-3x+\dfrac{1}{2}=2-\dfrac{4}{3}\)
=>\(-3x+\dfrac{1}{2}=\dfrac{6}{3}-\dfrac{4}{3}=\dfrac{2}{3}\)
=>\(-3x=\dfrac{2}{3}-\dfrac{1}{2}=\dfrac{4}{6}-\dfrac{3}{6}=\dfrac{1}{6}\)
=>\(x=\dfrac{1}{6}:\left(-3\right)=-\dfrac{1}{18}\)
14: \(\dfrac{3}{4}-\dfrac{5}{6}x=2-\dfrac{2}{3}\)
=>\(\dfrac{3}{4}-\dfrac{5}{6}x=\dfrac{4}{3}\)
=>\(\dfrac{5}{6}x=\dfrac{3}{4}-\dfrac{4}{3}=\dfrac{9}{12}-\dfrac{16}{12}=-\dfrac{7}{12}\)
=>\(x=-\dfrac{7}{12}:\dfrac{5}{6}=-\dfrac{7}{12}\cdot\dfrac{6}{5}=-\dfrac{7}{2\cdot5}=-\dfrac{7}{10}\)
