Answer
\[
\left\langle-\frac{2}{3}, 1\right\rangle
\]
Work Step by Step
The vectors are given as:
\[
\quad \vec{v}=\langle 2,1\rangle, \quad \vec{w}=\langle 4,-1\rangle, \vec{u}=\langle 1,3\rangle
\]
\[
-\vec{v}+\vec{x}+2 \vec{u}=\vec{w}+7 \vec{x}
\]
and then
\[
\begin{aligned}
6 \vec{x} &=-\vec{v}-\vec{w}+2 \vec{u} \\
&=-\langle 2,1\rangle-\langle 4,-1\rangle +2\langle 1,3\rangle\\
&=\langle-2,-1\rangle+\langle-4,1\rangle +\langle 2,6\rangle\\
&=\langle-4,6\rangle
\end{aligned}
\]
We have:
\[
\vec{x}= \langle-4,6\rangle \frac{1}{6}=\left\langle-\frac{2}{3}, 1\right\rangle
\]