Tìm \(x\), biết:

k) \[2\left( {x + \frac{1}{2}} \right) - 3\left( {x - \frac{4}{3}} \right) = - x + 1\].

e) \(\frac{{15}}{{37}} \cdot \left( {\frac{{38}}{{41}} - \frac{{74}}{{45}}} \right) - \frac{{38}}{{41}} \cdot \left( {\frac{{15}}{{37}} + \frac{{82}}{{76}}} \right)\)

\( = \frac{{15}}{{37}} \cdot \frac{{38}}{{41}} - \frac{{15}}{{37}} \cdot \frac{{74}}{{45}} - \frac{{38}}{{41}} \cdot \frac{{15}}{{37}} - \frac{{38}}{{41}} \cdot \frac{{82}}{{76}}\)

\[ = \left( {\frac{{15}}{{37}} \cdot \frac{{38}}{{41}} - \frac{{38}}{{41}} \cdot \frac{{15}}{{37}}} \right) + \left( { - \frac{{15}}{{37}} \cdot \frac{{74}}{{45}} - \frac{{38}}{{41}} \cdot \frac{{82}}{{76}}} \right)\]

\[ = 0 + \left( { - \frac{1}{1} \cdot \frac{2}{3} - \frac{{38}}{{41}} \cdot \frac{{41 \cdot 2}}{{38 \cdot 2}}} \right)\]

c) \(\frac{7}{4} - \left( {x + \frac{5}{3}} \right) = \frac{{ - 12}}{5}\)

\(x + \frac{5}{3} = \frac{7}{4} - \frac{{ - 12}}{5}\)

\(x + \frac{5}{3} = \frac{{83}}{{20}}\)

\(x = \frac{{83}}{{20}} - \frac{5}{3}\)

\(x = \frac{{149}}{{60}}\)