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Sum of the solutions of the equation $$[x] + 4 = 2x$$ is ($$[x]$$ denotes the greatest integer less than or equal to $$x$$)
Write $$x = n + f$$ with $$n = [x]$$ and $$0 \le f < 1$$. Then $$n + 4 = 2n + 2f$$, so $$2f = 4 - n$$. Since $$0 \le 2f < 2$$, either $$n = 4$$ (so $$f = 0$$, $$x = 4$$) or $$n = 3$$ (so $$f = \frac{1}{2}$$, $$x = 3.5$$). Sum of solutions $$= 4 + 3.5 = 7.5$$.
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