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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Sign up to join this communityI 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!
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,
$$-\frac12\le x<0.$$