7. (10 points) $\left[x-\frac{1}{2}\right]=3 x-5$, here $[x]$ represents the greatest integer not exceeding $x$, then $x=$

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【Analysis】According to the problem, for the original equation to hold, then $\left[x-\frac{1}{2}\right] \leqslant x-\frac{1}{2}, \Rightarrow 3 x-5 \leqslant x-\frac{1}{2}$, and $3 x-5$ is an integer, it is not difficult to find that $x=2$.

【Solution】Solution: According to the analysis, for the original equation to hold, then $\left[x-\frac{1}{2}\right] \leqslant x-\frac{1}{2}, \Rightarrow 3 x-5 \leqslant x-\frac{1}{2}, \Rightarrow x \leqslant \frac{9}{4}$, $\because 3 x-5 \geqslant 0 \therefore x=2$

Since $3 x-5$ is an integer, it is not difficult to find that $x=2$.
Therefore, the answer is: 2