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) \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\)
Chuyển các số hạng chứa ẩn sang một vế.
Chuyển các hằng số sang vế còn lại.
a) \(\frac{{2x}}{{15}} - \frac{{15 - 2x}}{{10}} = \frac{7}{6}\)
\(\frac{{4x}}{{30}} - \frac{{45 - 6x}}{{30}} = \frac{{35}}{{30}}\)
\(4x - 45 + 6x = 35\)
\(4x + 6x = 35 + 45\)
\(10x = 80\)
\(x = 8\)
Vậy \(x = 8\)
b) \(\frac{x}{{20}} - \frac{{x + 10}}{{25}} = 2\)
\(\frac{{5x}}{{100}} - \frac{{4x + 40}}{{100}} = \frac{{200}}{{100}}\)
\(5x - 4x - 40 = 200\)
\(x = 200 + 40\)
\(x = 240\)
Vậy \(x = 240\)
c) \(\frac{{2x - 37}}{3} = - 4x + 5\)
\(2x - 37 = 3\left( { - 4x + 5} \right)\)
\(2x - 37 = - 12x + 15\)
\(2x + 12x = 15 + 37\)
\(14x = 52\)
\(x = \frac{{26}}{7}\)
Vậy \(x = \frac{{26}}{7}\)
d) \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\)
\(\frac{{9\left( {3x + 1} \right) + 6}}{6} - \frac{{18}}{6} = \frac{{4\left( {5x + 1} \right)}}{6} - \frac{{3x + 1}}{6}\)
\(27x + 9 + 6 - 18 = 20x + 4 - 3x - 1\)
\(27x - 20x + 3x = 4 - 1 + 18 - 9\)
\(10x = 12\)
\(x = \frac{6}{5}\)
Vậy \(x = \frac{6}{5}\)