\(1)x=\dfrac{-1}{2}+\dfrac{3}{4}=\dfrac{-2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\\ 2)x-\dfrac{1}{5}=\dfrac{2}{11}\\ x=\dfrac{1}{5}+\dfrac{2}{11}=\dfrac{11}{55}+\dfrac{10}{55}=\dfrac{21}{55}\\ 3)x-\dfrac{5}{6}=\dfrac{16}{42}+\dfrac{-8}{56}=\dfrac{8}{21}+\dfrac{-3}{21}=\dfrac{5}{21}\\ x=\dfrac{5}{6}+\dfrac{5}{21}=\dfrac{15}{14}\\ 4)\dfrac{x}{6}=\dfrac{5}{6}+\dfrac{-19}{30}=\dfrac{1}{5}\\ x=6\cdot\dfrac{1}{5}=\dfrac{6}{5}\\ 5)\left|x\right|-\dfrac{1}{4}=\dfrac{6}{18}=\dfrac{1}{3}\\ \left|x\right|=\dfrac{1}{3}+\dfrac{1}{4}=\dfrac{7}{12}\\ x=\pm\dfrac{7}{12}\)
1: \(x=\dfrac{-1}{2}+\dfrac{3}{4}=\dfrac{-2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\)
2: \(x-\dfrac{1}{5}=\dfrac{2}{11}\)
=>\(x=\dfrac{2}{11}+\dfrac{1}{5}=\dfrac{10}{55}+\dfrac{11}{55}=\dfrac{21}{55}\)
3: \(x-\dfrac{5}{6}=\dfrac{16}{42}+\dfrac{-8}{56}\)
=>\(x-\dfrac{5}{6}=\dfrac{8}{21}+\dfrac{-1}{7}=\dfrac{5}{21}\)
=>\(x=\dfrac{5}{21}+\dfrac{5}{6}=\dfrac{10}{42}+\dfrac{35}{42}=\dfrac{45}{42}=\dfrac{15}{14}\)
4: \(\dfrac{x}{5}=\dfrac{5}{6}+\dfrac{-19}{30}\)
=>\(\dfrac{x}{5}=\dfrac{25}{30}-\dfrac{19}{60}=\dfrac{6}{30}=\dfrac{1}{5}\)
=>x=1
5: \(\left|x\right|-\dfrac{1}{4}=\dfrac{6}{18}\)
=>\(\left|x\right|-\dfrac{1}{4}=\dfrac{1}{3}\)
=>\(\left|x\right|=\dfrac{1}{4}+\dfrac{1}{3}=\dfrac{7}{12}\)
=>\(\left[{}\begin{matrix}x=\dfrac{7}{12}\\x=-\dfrac{7}{12}\end{matrix}\right.\)
6: \(x=\dfrac{-1}{2}+\dfrac{3}{4}=\dfrac{-2}{4}+\dfrac{3}{4}=\dfrac{1}{4}\)
7: \(\dfrac{x}{15}=\dfrac{3}{5}+\dfrac{-2}{3}\)
=>\(\dfrac{x}{15}=\dfrac{9}{15}-\dfrac{10}{15}=-\dfrac{1}{15}\)
=>x=-1
8: \(\dfrac{11}{8}+\dfrac{13}{6}=\dfrac{85}{x}\)
=>\(\dfrac{85}{x}=\dfrac{33}{24}+\dfrac{52}{24}=\dfrac{85}{24}\)
=>x=24
9: \(x-\dfrac{7}{8}=\dfrac{13}{12}\)
=>\(x=\dfrac{13}{12}+\dfrac{7}{8}=\dfrac{26}{24}+\dfrac{21}{24}=\dfrac{47}{24}\)
10: \(x-\dfrac{-6}{15}=\dfrac{4}{27}\)
=>\(x+\dfrac{2}{5}=\dfrac{4}{27}\)
=>\(x=\dfrac{4}{27}-\dfrac{2}{5}=\dfrac{20}{135}-\dfrac{54}{135}=-\dfrac{34}{135}\)
11: \(-\dfrac{-6}{12}+x=\dfrac{9}{48}\)
=>\(x+\dfrac{1}{2}=\dfrac{3}{16}\)
=>\(x=\dfrac{3}{16}-\dfrac{1}{2}=-\dfrac{5}{16}\)
12: \(x-\dfrac{4}{6}=\dfrac{5}{25}+\dfrac{-7}{15}\)
=>\(x-\dfrac{2}{3}=\dfrac{1}{5}+\dfrac{-7}{15}=\dfrac{-4}{15}\)
=>\(x=-\dfrac{4}{15}+\dfrac{2}{3}=-\dfrac{4}{15}+\dfrac{10}{15}=\dfrac{6}{15}=\dfrac{2}{5}\)