(1,25 điểm) Tìm \(x\), biết:

a) \(3x - \frac{2}{3} = \frac{5}{7}\);       b) \(\left| {\frac{1}{4}x + 0,75} \right| - 2\frac{1}{5} = - \frac{3}{{10}}\).

a) \(3x - \frac{2}{3} = \frac{5}{7}\)

    \(3x = \frac{5}{7} + \frac{2}{3}\)

    \(3x = \frac{{29}}{{21}}\)

      \(x = \frac{{29}}{{21}}:3\)

      \(x = \frac{{29}}{{63}}\).

Vậy \(x = \frac{{29}}{{63}}\).

b) \(\left| {\frac{1}{4}x + 0,75} \right| - 2\frac{1}{5} =  - \frac{3}{{10}}\)

    \(\left| {\frac{1}{4}x + \frac{3}{4}} \right| =  - \frac{3}{{10}} + 2\frac{1}{5}\)

    \(\left| {\frac{1}{4}x + \frac{3}{4}} \right| =  - \frac{3}{{10}} + \frac{{11}}{5} = \frac{{19}}{{10}}\)

Trường hợp 1:

\(\frac{1}{4}x + \frac{3}{4} = \frac{{19}}{{10}}\)         

\(\frac{1}{4}x = \frac{{19}}{{10}} - \frac{3}{4}\)

\(\frac{1}{4}x = \frac{{23}}{{20}}\)

\(x = \frac{{23}}{{20}}:\frac{1}{4}\)

\(x = \frac{{23}}{5}\)

Vậy \(x \in \left\{ {\frac{{23}}{5}; - \frac{{53}}{5}} \right\}\)

Trường hợp 2:

\(\frac{1}{4}x + \frac{3}{4} =  - \frac{{19}}{{10}}\)

\(\frac{1}{4}x =  - \frac{{19}}{{10}} - \frac{3}{4}\)

\(\frac{1}{4}x =  - \frac{{53}}{{20}}\)

\(x =  - \frac{{53}}{{20}}:\frac{1}{4}\)

\(x =  - \frac{{53}}{5}\)