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How can I solve an equation with multiple floor functions added together?

$$ 18 + \lfloor 2.6 \rfloor + \lfloor x \rfloor + \left\lfloor \frac x4 \right\rfloor + 5 = 1 $$

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closed as off-topic by Saad, steven gregory, M. Vinay, Xander Henderson, Alex Provost Mar 14 at 19:38

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    $\begingroup$ Welcome to Math Stack Exchange. Floor(2.6)=2, right? $\endgroup$ – J. W. Tanner Mar 14 at 12:46
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$\lfloor x\rfloor+\lfloor x/4\rfloor=-24$. Use the fact $m-1<\lfloor m\rfloor\le m$ to conclude $5x/4-2<-24\le5x/4$. Solve these simultaneous inequalities to narrow down the search to the interval $[-19.2,-17.6)$. Note that $\lfloor x/4\rfloor=-5$ in the entire interval, so you need the subset where $\lfloor x\rfloor=-19$, i.e.$[-19,-18)$.

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