Đáp án:

\(\begin{array}{l}
a,\,\,\,\,x =  - \dfrac{{65}}{6}\\
b,\,\,\,\,x = \dfrac{2}{7}\\
c,\,\,\,\,x = \dfrac{9}{{10}}\\
d,\,\,\,\,x = 4\\
e,\,\,\,\,x =  - \dfrac{3}{4}\\
f,\,\,\,\,x =  - \dfrac{{25}}{8}\\
g,\,\,\,\,x = \dfrac{{51}}{2}\\
h,\,\,\,\,x = \dfrac{2}{3}\\
i,\,\,\,\,x = \dfrac{{11}}{{20}}\\
j,\,\,\,\,x =  - \dfrac{{17}}{8}\\
k,\,\,\,\,x = \dfrac{{11}}{{20}}\\
l,\,\,\,\,x = \dfrac{3}{2}\\
m,\,\,\,\,x =  - \dfrac{1}{4}\\
n,\,\,\,\,x = \dfrac{1}{2}
\end{array}\)

Giải thích các bước giải:

Ta có:

\(\begin{array}{l}
a,\\
x:4\dfrac{1}{3} =  - 2,5\\
 \Leftrightarrow x:\dfrac{{13}}{3} =  - \dfrac{5}{2}\\
 \Leftrightarrow x = \left( { - \dfrac{5}{2}} \right).\dfrac{{13}}{3}\\
 \Leftrightarrow x =  - \dfrac{{65}}{6}\\
b,\\
x:\dfrac{{ - 3}}{5} = \dfrac{{ - 10}}{{21}}\\
 \Leftrightarrow x = \left( {\dfrac{{ - 10}}{{21}}} \right).\left( {\dfrac{{ - 3}}{5}} \right)\\
 \Leftrightarrow x = \dfrac{{10}}{{21}}.\dfrac{3}{5}\\
 \Leftrightarrow x = \dfrac{2}{7}\\
c,\\
\dfrac{2}{3}x - \dfrac{1}{2} = \dfrac{1}{{10}}\\
 \Leftrightarrow \dfrac{2}{3}x = \dfrac{1}{{10}} + \dfrac{1}{2}\\
 \Leftrightarrow \dfrac{2}{3}x = \dfrac{3}{5}\\
 \Leftrightarrow x = \dfrac{3}{5}:\dfrac{2}{3}\\
 \Leftrightarrow x = \dfrac{9}{{10}}\\
d,\\
\dfrac{1}{2}x + \dfrac{1}{2} = \dfrac{5}{2}\\
 \Leftrightarrow \dfrac{1}{2}x = \dfrac{5}{2} - \dfrac{1}{2}\\
 \Leftrightarrow \dfrac{1}{2}x = 2\\
 \Leftrightarrow x = 2:\dfrac{1}{2}\\
 \Leftrightarrow x = 4\\
e,\\
\dfrac{{ - 2}}{3} - \dfrac{1}{3}\left( {2x - 5} \right) = \dfrac{3}{2}\\
 \Leftrightarrow \dfrac{1}{3}\left( {2x - 5} \right) = \dfrac{{ - 2}}{3} - \dfrac{3}{2}\\
 \Leftrightarrow \dfrac{1}{3}\left( {2x - 5} \right) =  - \dfrac{{13}}{6}\\
 \Leftrightarrow 2x - 5 = \left( { - \dfrac{{13}}{6}} \right):\dfrac{1}{3}\\
 \Leftrightarrow 2x - 5 =  - \dfrac{{13}}{2}\\
 \Leftrightarrow 2x =  - \dfrac{{13}}{2} + 5\\
 \Leftrightarrow 2x =  - \dfrac{3}{2}\\
 \Leftrightarrow x = \left( { - \dfrac{3}{2}} \right):2\\
 \Leftrightarrow x =  - \dfrac{3}{4}\\
f,\\
\dfrac{2}{5}x + \dfrac{1}{2} =  - \dfrac{3}{4}\\
 \Leftrightarrow \dfrac{2}{5}x =  - \dfrac{3}{4} - \dfrac{1}{2}\\
 \Leftrightarrow \dfrac{2}{5}x =  - \dfrac{5}{4}\\
 \Leftrightarrow x = \left( { - \dfrac{5}{4}} \right):\dfrac{2}{5}\\
 \Leftrightarrow x =  - \dfrac{{25}}{8}\\
g,\\
\dfrac{1}{3}x - 8 = \dfrac{1}{2}\\
 \Leftrightarrow \dfrac{1}{3}x = \dfrac{1}{2} + 8\\
 \Leftrightarrow \dfrac{1}{3}x = \dfrac{{17}}{2}\\
 \Leftrightarrow x = \dfrac{{17}}{2}:\dfrac{1}{3}\\
 \Leftrightarrow x = \dfrac{{51}}{2}\\
h,\\
x - \dfrac{1}{4} = \dfrac{5}{8}.\dfrac{2}{3}\\
 \Leftrightarrow x - \dfrac{1}{4} = \dfrac{5}{{12}}\\
 \Leftrightarrow x = \dfrac{5}{{12}} + \dfrac{1}{4}\\
 \Leftrightarrow x = \dfrac{2}{3}\\
i,\\
\dfrac{3}{4} - x = \dfrac{1}{5}\\
 \Leftrightarrow x = \dfrac{3}{4} - \dfrac{1}{5}\\
 \Leftrightarrow x = \dfrac{{11}}{{20}}\\
j,\\
\dfrac{7}{2} + 2x = \dfrac{{ - 3}}{4}\\
 \Leftrightarrow 2x = \dfrac{{ - 3}}{4} - \dfrac{7}{2}\\
 \Leftrightarrow 2x =  - \dfrac{{17}}{4}\\
 \Leftrightarrow x = \left( { - \dfrac{{17}}{4}} \right):2\\
 \Leftrightarrow x =  - \dfrac{{17}}{8}\\
k,\\
\dfrac{3}{4} - x = \dfrac{1}{5}\\
 \Leftrightarrow x = \dfrac{3}{4} - \dfrac{1}{5}\\
 \Leftrightarrow x = \dfrac{{11}}{{20}}\\
l,\\
\dfrac{1}{3} + \dfrac{2}{3}x = \dfrac{4}{3}\\
 \Leftrightarrow \dfrac{2}{3}x = \dfrac{4}{3} - \dfrac{1}{3}\\
 \Leftrightarrow \dfrac{2}{3}x = 1\\
 \Leftrightarrow x = 1:\dfrac{2}{3}\\
 \Leftrightarrow x = \dfrac{3}{2}\\
m,\\
\dfrac{3}{5}x + \dfrac{1}{4} = \dfrac{1}{{10}}\\
 \Leftrightarrow \dfrac{3}{5}x = \dfrac{1}{{10}} - \dfrac{1}{4}\\
 \Leftrightarrow \dfrac{3}{5}x =  - \dfrac{3}{{20}}\\
 \Leftrightarrow x = \left( { - \dfrac{3}{{20}}} \right):\dfrac{3}{5}\\
 \Leftrightarrow x =  - \dfrac{1}{4}\\
n,\\
 - \dfrac{4}{3}x + \dfrac{3}{2} = \dfrac{5}{6}\\
 \Leftrightarrow  - \dfrac{4}{3}x = \dfrac{5}{6} - \dfrac{3}{2}\\
 \Leftrightarrow  - \dfrac{4}{3}x =  - \dfrac{2}{3}\\
 \Leftrightarrow \dfrac{4}{3}x = \dfrac{2}{3}\\
 \Leftrightarrow x = \dfrac{2}{3}:\dfrac{4}{3}\\
 \Leftrightarrow x = \dfrac{1}{2}
\end{array}\)