I am trying to solve the following problem:
For what real numbers x is: ⌊2x⌋=4⌊x⌋+3?
I'm not sure how to deal with the floor functions, so I have no idea where to start. If someone could walk me through the process that would great!
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$\begingroup$ Welcome to MSE. For some basic information about writing mathematics at this site see, e.g., basic help on mathjax notation, mathjax tutorial and quick reference, main meta site math tutorial and equation editing how-to. $\endgroup$ – José Carlos Santos Sep 28 '19 at 9:18
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Notice that $\lfloor 2x\rfloor=2\lfloor x\rfloor$ or $\lfloor 2x\rfloor=2\lfloor x\rfloor+1$ depending on the fractional part. Plugging in the equation, we get
$$\lfloor x\rfloor=-\frac32$$ which is not possible or
$$\lfloor x\rfloor=-1.$$
Hence,
$$-\frac12\le x<0.$$
answered Sep 28 '19 at 10:25
