Hướng dẫn giải:

a) \(\frac{2}{3}.x + \frac{1}{2} = \frac{1}{{10}}\)

\(\frac{2}{3}.x = \frac{1}{{10}} - \frac{1}{2}\)

\(\frac{2}{3}.x = \frac{1}{{10}} - \frac{5}{{10}}\)

\(\frac{2}{3}.x = \frac{{ - 4}}{{10}}\)

\(\frac{2}{3}.x = \frac{{ - 2}}{5}\)

\(x = \frac{{ - 2}}{5}:\frac{2}{3}\)

\(x = \frac{{ - 2}}{5}.\frac{3}{2}\)

\(x = \frac{{ - 3}}{5}\)

Vậy \(x = \frac{{ - 3}}{5}\)

b) \[\left( {4\frac{1}{2} - 2x} \right).1\frac{4}{{61}} = 6\frac{1}{2}\].

\[\left( {\frac{9}{2} - 2x} \right).\frac{{65}}{{61}} = \frac{{13}}{2}\]

\[\frac{9}{2} - 2x = \frac{{13}}{2}:\frac{{65}}{{61}}\]

\[\frac{9}{2} - 2x = \frac{{13}}{2}.\frac{{61}}{{65}}\]

\[\frac{9}{2} - 2x = \frac{{13}}{2}.\frac{{61}}{{5.13}}\]

\[\frac{9}{2} - 2x = \frac{{61}}{{10}}\]

\[2x = \frac{9}{2} - \frac{{61}}{{10}}\]

\[2x = \frac{{45}}{{10}} - \frac{{61}}{{10}}\]

\[2x = \frac{{ - 16}}{{10}}\]

\[2x = \frac{{ - 8}}{5}\]

\[x = \frac{{ - 8}}{5}:2\]

\[x = \frac{{ - 8}}{5}.\frac{1}{2}\]

\[x = \frac{{ - 4}}{5}\]

Vậy \[x = \frac{{ - 4}}{5}\].

c) x – 83%.x = –1,7

\(x - \frac{{83}}{{100}}.x = - \frac{{17}}{{10}}\)

\(x.\left( {1 - \frac{{83}}{{100}}} \right) = - \frac{{17}}{{10}}\)

\(x.\frac{{100 - 83}}{{100}} = - \frac{{17}}{{10}}\)

\(x.\frac{{17}}{{100}} = \frac{{ - 17}}{{10}}\)

\(x = \frac{{ - 17}}{{10}}:\frac{{17}}{{100}}\)

\(x = \frac{{ - 17}}{{10}}.\frac{{100}}{{17}}\)

x = 10.

Vậy x = 10.

Số nghịch đảo của –0,4 là: