1. a) \[\frac{{ - 2}}{3} + \frac{4}{5}\, + \frac{{ - 5}}{3} - \frac{{19}}{5} = \left( {\frac{{ - 2}}{3} + \frac{{ - 5}}{3}} \right) + \left( {\frac{4}{5}\, - \frac{{19}}{5}} \right)\]

\[ = \frac{{ - 7}}{3} + \left( { - 3} \right) = \frac{{ - 7}}{3} - \frac{9}{3} = \frac{{ - 16}}{3}\].

b) \[12\,\,.\,\,{\left( {\frac{3}{2}} \right)^2} + {\left( {\frac{{25}}{6}} \right)^0}\,\,.\,\,\frac{{15}}{2} - 9\frac{1}{4} = 12\,\,.\,\,\frac{9}{4} + 1\,\,.\,\,\frac{{15}}{2} - \frac{{37}}{4}\]

\[ = 12\,\,.\,\,\frac{9}{4} + 1\,\,.\,\,\frac{{15}}{2} - \frac{{37}}{4} = 27 + \frac{{15}}{2} - \frac{{37}}{4} = \frac{{69}}{2} - \frac{{37}}{4} = \frac{{101}}{4}\].

2. a) \(\frac{{ - 3}}{8} + \frac{5}{6}x = \frac{{ - 17}}{{12}}\)

\(\frac{5}{6}x = \frac{{ - 17}}{{12}} + \frac{3}{8}\)

\(\frac{5}{6}x = \frac{{ - 25}}{{24}}\)

\(x = \frac{{ - 25}}{{24}}:\frac{5}{6}\)

\(x = \frac{{ - 5}}{4}\).

Vậy \(x = \frac{{ - 5}}{4}\).

b) \({\left( {\frac{1}{2}} \right)^3} - \left( {x + \frac{2}{5}} \right)\,:\frac{2}{3} = \frac{{ - 31}}{{40}}\)

\(\frac{1}{8} - \left( {x + \frac{2}{5}} \right)\,\,\,.\,\,\frac{3}{2} = \frac{{ - 31}}{{40}}\)

\(\left( {x + \frac{2}{5}} \right)\,\,\,.\,\,\frac{3}{2} = \frac{1}{8} + \frac{{31}}{{40}}\)

\(\left( {x + \frac{2}{5}} \right)\,\,\,.\,\,\frac{3}{2} = \frac{9}{{10}}\)

\(x + \frac{2}{5}\, = \frac{9}{{10}}:\,\frac{3}{2}\)

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

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

\(x\, = \frac{1}{5}\)

Vậy \(x\, = \frac{1}{5}\).

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