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Question Number 185981 by mnjuly1970 last updated on 30/Jan/23

$$$$$$solvein\mathbb{R}$$$$$$$$\lfloor 2x\rfloor +\lfloor 3x\rfloor =1$$$$$$$$\lfloor x\rfloor :=greatestintegernumber$$$$morethanorequalto{}^{″}x{}^{″}$$

Answered by mr W last updated on 30/Jan/23

$$x=n+f$$$$5n+\lfloor 2f\rfloor +\lfloor 3f\rfloor =1$$$$1-5n=\lfloor 2f\rfloor +\lfloor 3f\rfloor ⩾0\Rightarrow n⩽0$$$$1-5n=\lfloor 2f\rfloor +\lfloor 3f\rfloor <5\Rightarrow n⩾0$$$$\Rightarrow n=0\Rightarrow 0⩽x<1$$$$2x<1\Rightarrow x<\frac{1}{2}$$$$1⩽3x<2\Rightarrow \frac{1}{3}⩽x<\frac{2}{3}$$$$\Rightarrow \frac{1}{3}⩽x<\frac{1}{2}✓$$

Commented by mnjuly1970 last updated on 31/Jan/23

$$merceysirW..$$

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