Giải các phương trình:
a) \(\frac{{2x}}{{15}} - \frac{{15 - 2x}}{{10}} = \frac{7}{6}\)
b) \(\frac{x}{{20}} - \frac{{x + 10}}{{25}} = 2\)
c) \(\frac{{2x - 37}}{3} = - 4x + 5\)
d) \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\)
Áp dụng các quy tắc tính để giải phương trình
a) \(\frac{{2x}}{{15}} - \frac{{15 - 2x}}{{10}} = \frac{7}{6}\)
\( \frac{{4x}}{{30}} - \frac{{45 - 6x}}{{30}} = \frac{{35}}{{30}}\)
\( 4x - 45 + 6x = 35\)
\( 10x = 80\)
\( x = 8\)
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b) \(\frac{x}{{20}} - \frac{{x + 10}}{{25}} = 2\)
\( 5x - 4\left( {x + 10} \right) = 200\)
\( x - 40 = 200\)
\( x = 240\)
c) \(\frac{{2x - 37}}{3} = - 4x + 5\)
\( 2x - 37 = 3\left( { - 4x + 5} \right)\)
\( 14x = 52\)
\( x = \frac{{26}}{7}\)
d) \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\)
\( \frac{{3\left[ {3\left( {3x + 1} \right) + 2} \right]}}{6} - \frac{{18}}{6} = \frac{{4\left( {5x + 1} \right)}}{6} - \frac{{3x + 1}}{6}\)
\( 9\left( {3x + 1} \right) + 6 - 18 = 4\left( {5x + 1} \right) - 3x - 1\)
\( 10x = 6\)
\( x = 0,6\)