Answer
\[
\left\langle\frac{2}{3}, \frac{2}{3}\right\rangle
\]
Work Step by Step
The vectors are given as:
\[
\quad \vec{v}=\langle 0,1\rangle,
\vec{u}=\langle-1,1\rangle, \quad \text { and } \quad \vec{w}=\langle 3,4\rangle
\]
We need to find the $\vec {x}$ vector:
\[
-2 \vec{x}+\vec{u}=-\vec{w}+3 \vec{v}+\vec{x}
\]
and then
\[
\begin{aligned}
2 \vec{x}+ \vec{x} &=\vec{w}-3 \vec{v}+\vec{u} \\
3 \vec{x} &=\langle 3,4\rangle-3\langle 0,1\rangle+\langle-1,1\rangle \\
&=\langle-1+3-0,1+4-3\rangle=\langle 2,2\rangle
\end{aligned}
\]
So we have that
\[
\vec{x}=\frac{1}{3}\langle 2,2\rangle=\left\langle\frac{2}{3}, \frac{2}{3}\right\rangle
\]
