Đề bài

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)     \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\)

Lời giải chi tiết

a)      \(\frac{{2x}}{{15}} - \frac{{15 - 2x}}{{10}} = \frac{7}{6}\) \( \frac{{4x}}{{30}} - \frac{{45 - 6x}}{{30}} = \frac{{35}}{{30}}\) \( 4x - 45 + 6x = 35\) \( 10x = 80\) \( x = 8\) 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)     \(\frac{{3\left( {3x + 1} \right) + 2}}{2} - 3 = \frac{{2\left( {5x + 1} \right)}}{3} - \frac{{3x + 1}}{6}\) \( \frac{{3\left[ {3\left( {3x + 1} \right) + 2} \right]}}{6} - \frac{{18}}{6} = \frac{{4\left( {5x + 1} \right)}}{6} - \frac{{3x + 1}}{6}\) \( 9\left( {3x + 1} \right) + 6 - 18 = 4\left( {5x + 1} \right) - 3x - 1\) \( 10x = 6\) \( x = 0,6\)