\begin{enumerate}
\begin{multicols}{2}
\item $\begin{aligned}[t]
3x-7&=4x+1\\
3x-4x&=1+7\\
-x&=8\\
\Aboxed{x&=-8}
\end{aligned}$

\item $\begin{aligned}[t]
\dfrac{1}{2}x-8&=9x-1\\
\dfrac{1}{2}x-9x&=-1+8\\
\dfrac{1}{2}x-\dfrac{18}{2}x&=7\\
-\dfrac{17}{2}x&=7\\
x&=7\times\left(-\dfrac{2}{17}\right)\\
\Aboxed{x&=-\dfrac{14}{17}}
\end{aligned}$

\item $\begin{aligned}[t]
-\dfrac{1}{3}x+4&=\dfrac{1}{2}x-4\\
-\dfrac{1}{3}x-\dfrac{1}{2}x&=-4-4\\
-\dfrac{2}{6}x-\dfrac{3}{6}x&=-8\\
-\dfrac{5}{6}x&=-8\\
x&=-8\times\left(-\dfrac{6}{5}\right)\\
\Aboxed{x&=\dfrac{48}{5}}
\end{aligned}$

\item $\begin{aligned}[t]
\dfrac{x-9}{2}+\dfrac{2x+4}{5}&=-5\\
\dfrac{5(x-9)}{10}+\dfrac{2(2x+4)}{10}&=\dfrac{-50}{10}\\
5(x-9)+2(2x+4)&=-50\\
5x-45+4x+8&=-50\\
9x&=-50+45-8\\
9x&=-13\\
\Aboxed{x&=-\dfrac{13}{9}}
\end{aligned}$

\item $\begin{aligned}[t]
\dfrac{3x-7}{7}-\dfrac{2x+1}{2}&=1\\
\dfrac{2(3x-7)}{14}-\dfrac{7(2x+1)}{14}&=\dfrac{14}{14}\\
2(3x-7)-7(2x+1)&=14\\
6x-14-14x-7&=14\\
6x-14x&=14+14+7\\
-8x&=35\\
\Aboxed{x&=-\dfrac{35}{8}}
\end{aligned}$

\item $\begin{aligned}[t]
\dfrac{4x-1}{5}+\dfrac{7x-8}{4}&=3\\
\dfrac{4(4x-1)}{20}+\dfrac{5(7x-8)}{20}&=\dfrac{3\times20}{20}\\
4(4x-1)+5(7x-8)&=60\\
16x-4+35x-40&=60\\
16x+35x&=60+4+40\\
51x&=104\\
\Aboxed{x&=\dfrac{104}{51}}
\end{aligned}$
\end{multicols}
\end{enumerate}