Đáp án:
$\begin{array}{l}
7)a)\dfrac{{3x + 2}}{2} - \dfrac{{3x + 1}}{6} = 2x + \dfrac{5}{3}\\
\Rightarrow \dfrac{{3\left( {3x + 2} \right) - 3x - 1}}{6} = \dfrac{{12x + 10}}{6}\\
\Rightarrow 9x + 6 - 3x - 1 = 12x + 10\\
\Rightarrow 12x - 9x + 3x = 6 - 1 - 10\\
\Rightarrow 6x = - 5\\
\Rightarrow x = - \dfrac{5}{6}\\
Vậy\,x = - \dfrac{5}{6}\\
b)x - \dfrac{{2x - 5}}{5} + \dfrac{{x + 8}}{6} = 7 + \dfrac{{x - 1}}{3}\\
\Rightarrow \dfrac{{30x - 6\left( {2x - 5} \right) + 5\left( {x + 8} \right)}}{{30}} = \dfrac{{7.30 + 10\left( {x - 1} \right)}}{{30}}\\
\Rightarrow 30x - 12x + 30 + 5x + 40\\
= 210x + 10x - 10\\
\Rightarrow 197x = 80\\
\Rightarrow x = \dfrac{{80}}{{197}}\\
Vậy\,x = \dfrac{{80}}{{197}}\\
c)\dfrac{{5x + 2}}{6} - \dfrac{{8x - 1}}{3} = \dfrac{{4x + 2}}{5} - 5\\
\Rightarrow \dfrac{{5\left( {5x + 2} \right) - 10\left( {8x - 1} \right)}}{{30}} = \dfrac{{6\left( {4x + 2} \right) - 5.30}}{{30}}\\
\Rightarrow 25x + 10 - 80x + 10 = 24x + 12 - 150\\
\Rightarrow 79x = 158\\
\Rightarrow x = 2\\
Vậy\,x = 2\\
8)a)\dfrac{{x + 1}}{{15}} + \dfrac{{x + 2}}{7} + \dfrac{{4x + 2}}{5} + 6 = 0\\
\Rightarrow \dfrac{{7\left( {x + 1} \right) + 15\left( {x + 2} \right) + 21\left( {4x + 2} \right) + 6.105}}{{105}} = 0\\
\Rightarrow 7x + 7 + 15x + 30 + 84x + 42 + 630 = 0\\
\Rightarrow 106x = - 709\\
\Rightarrow x = - \dfrac{{709}}{{106}}\\
Vậy\,x = - \dfrac{{709}}{{106}}\\
b)\\
\dfrac{{x + 14}}{{200}} + \dfrac{{x + 27}}{{187}} + \dfrac{{x + 105}}{{109}}\\
= \dfrac{{x + 200}}{{14}} + \dfrac{{x + 187}}{{27}} + \dfrac{{x + 109}}{{105}}\\
\Rightarrow \dfrac{{x + 14}}{{200}} + 1 + \dfrac{{x + 27}}{{187}} + 1 + \dfrac{{x + 105}}{{109}} + 1\\
= \dfrac{{x + 200}}{{14}} + 1 + \dfrac{{x + 187}}{{27}} + 1 + \dfrac{{x + 109}}{{105}} + 1\\
\Rightarrow \dfrac{{x + 214}}{{200}} + \dfrac{{x + 214}}{{187}} + \dfrac{{x + 214}}{{109}}\\
= \dfrac{{x + 214}}{{14}} + \dfrac{{x + 214}}{{27}} + \dfrac{{x + 214}}{{105}}\\
\Rightarrow \left( {x + 214} \right)\left( {\dfrac{1}{{200}} + \dfrac{1}{{187}} + \dfrac{1}{{109}} - \dfrac{1}{{14}} - \dfrac{1}{{27}} - \dfrac{1}{{105}}} \right) = 0\\
\Rightarrow x = - 214\\
Vậy\,x = - 214
\end{array}$
