Giải các phương trình sau:

a) $2x - 4 = 3x + 1$

b) $7\left( {5 - x} \right) = 11 - 5x$

c) $\frac{5}{6} + \frac{x}{4} = 2 - \frac{x}{3}$

d) $\frac{{2\left( {x + 1} \right)}}{3} = \frac{{1 + 3x}}{4} + \frac{1}{2}$

a) $2x - 4 = 3x + 1$

$\begin{array}{l}2x - 3x = 1 + 4\\ - x = 5\\x =  - 5\end{array}$

Vậy $x =  - 5$.

b) $7\left( {5 - x} \right) = 11 - 5x$

$\begin{array}{l}35 - 7x = 11 - 5x\\ - 7x + 5x = 11 - 35\\ - 2x =  - 24\\x = 12\end{array}$

Vậy $x = 12$.

c) $\frac{5}{6} + \frac{x}{4} = 2 - \frac{x}{3}$

$\begin{array}{l}\frac{{10}}{{12}} + \frac{{3x}}{{12}} = \frac{{24}}{{12}} - \frac{{4x}}{{12}}\\10 + 3x = 24 - 4x\\3x + 4x = 24 - 10\\7x = 14\\x = 2\end{array}$

Vậy $x = 2$.

d) $\frac{{2\left( {x + 1} \right)}}{3} = \frac{{1 + 3x}}{5} + \frac{1}{2}$

$\begin{array}{l}\frac{{10.2\left( {x + 1} \right)}}{{30}} = \frac{{6\left( {1 + 3x} \right)}}{{30}} + \frac{{15}}{{30}}\\20\left( {x + 1} \right) = 6\left( {1 + 3x} \right) + 15\\20x + 20 = 6 + 18x + 15\\20x - 18x = 6 + 15 - 20\\2x = 1\\x = \frac{1}{2}\end{array}$

Vậy $x = \frac{1}{2}$.