Đáp án:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \frac{9}{70} \ b.\ \frac{13}{50} ;\ c.\ \frac{-5}{71} ;\ d.\ \frac{1}{2} ;\ e.\ 1\\ f.\ \frac{-14}{15} ;\ g.\ -\frac{7}{30} ;\ h.\ \frac{23}{4} ;\ i.\ -\frac{16}{45} ;\ k.\ \frac{-43}{7} \end{array}$
Giải thích các bước giải:
$\displaystyle \begin{array}{{>{\displaystyle}l}} a.\ \frac{3}{2} x-\frac{2}{5} =\frac{1}{3} x-\frac{1}{4}\\ \Leftrightarrow \frac{3}{2} x-\frac{1}{3} x=-\frac{1}{4} +\frac{2}{5}\\ \Leftrightarrow \frac{7}{6} x=\frac{3}{20}\\ \Leftrightarrow x=\frac{9}{70}\\ b.\ 2x-\frac{1}{4} =\frac{5}{6} -\frac{1}{2} x\\ \Leftrightarrow 2x+\frac{1}{2} x=\frac{5}{6} +\frac{1}{4}\\ \Leftrightarrow \frac{5}{2} x=\frac{13}{12}\\ \Leftrightarrow x=\frac{13}{30}\\ c.\ \frac{2}{3} -\frac{5}{3} x=\frac{7}{10} x+\frac{5}{6}\\ \Leftrightarrow \frac{-5}{3} x-\frac{7}{10} x=\frac{5}{6} -\frac{2}{3}\\ \Leftrightarrow \frac{-71}{30} x=\frac{1}{6}\\ \Leftrightarrow x=\frac{-5}{71}\\ d.\ \frac{1}{2}( x+2) -4\left( x-\frac{1}{4}\right) =\frac{1}{2} x\\ \Leftrightarrow \frac{1}{2} x-4x-\frac{1}{2} x=-2\\ \Leftrightarrow -4x=-2\\ \Leftrightarrow x=\frac{1}{2}\\ e.\ \frac{5}{3} .( 3x-3) +\frac{1}{2} =\frac{1}{2}( 2x-1)\\ \Leftrightarrow 5x-5+\frac{1}{2} =x-\frac{1}{2}\\ \Leftrightarrow 4x=4\\ \Leftrightarrow x=1\\ f.\ \frac{5}{2} .\left( x-\frac{3}{5}\right) -\frac{1}{10} =x-3\\ \Leftrightarrow \frac{5}{2} x-\frac{3}{2} -\frac{1}{10} =x-3\\ \Leftrightarrow \frac{5}{2} x-x=-3+\frac{1}{10} +\frac{3}{2}\\ \Leftrightarrow \frac{3}{2} x=\frac{-7}{5}\\ \Leftrightarrow x=\frac{-14}{15}\\ g,\ 2x-\frac{2}{3} -7x=\frac{3}{2} -1\\ \Leftrightarrow -5x=\frac{7}{6}\\ \Leftrightarrow x=\frac{7}{6} :( -5) =\frac{-7}{30}\\ h.\ 4-\frac{2}{3} .( x-3) =2-\frac{1}{2} +\frac{2}{3}\\ \Leftrightarrow 4-\frac{2}{3} x+2=\frac{13}{6}\\ \Leftrightarrow -\frac{2}{3} x=\frac{-23}{6}\\ \Leftrightarrow x=\frac{23}{4}\\ i.\ -\frac{3}{4} .\left(\frac{8}{9} -x\right) +\frac{3}{5} =-\frac{2}{3} .\frac{1}{2}\\ \Leftrightarrow -\frac{2}{3} +\frac{3}{4} x+\frac{3}{5} =-\frac{1}{3}\\ \Leftrightarrow \frac{3}{4} x=-\frac{4}{15}\\ \Leftrightarrow x=-\frac{16}{45}\\ k.\ \frac{2}{3} .\left( x-\frac{9}{4}\right) =\frac{3}{7} .\left( 7-\frac{1}{6}\right) -\frac{1}{3}\\ \Leftrightarrow \frac{2}{3} x-\frac{3}{2} =\frac{41}{14} -\frac{1}{3}\\ \Leftrightarrow -\frac{2}{3} x=\frac{109}{42} +\frac{3}{2} =\frac{86}{21}\\ \Leftrightarrow x=-\frac{43}{7} \end{array}$
