# Formula containing floor functions. [closed]

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

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

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

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• Welcome to Math Stack Exchange. Floor(2.6)=2, right? – J. W. Tanner Mar 14 at 12:46

$$\lfloor x\rfloor+\lfloor x/4\rfloor=-24$$. 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.$$[-19,-18)$$.