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This is a homework puzzle so I'm not asking for the direct answer.

Find all numbers $x$ in $\Bbb R$ for:

$[x+2] = 6[x] - 23$

I haven't see greatest integer functions that have a scalar out the front nor two GIF in one function. Could someone please help me understand how to solve this? :)

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    Sketch a graph? Or note that each side of the equation will always be an integer, so solve for $x$ an integer, and then consider the range of solutions around that.2012-03-15

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I think it's long enough that I can add a full answer. By the first hint, you have that,

$\begin{align}[x+2]\overset{1}{=}[x]+2&=6[x]-23\\5[x]&=25\\\ [x]&=5\\(2) \implies 5\le &x \lt6\end{align}$

So, the solution is $\boxed{5 \le x \lt6}$


Hint:

  1. $[x+I]=[x]+I$ for $I$ an integer.
  2. $[x]=I \implies I\le x \lt I+1$ for $I$ an integer.
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    Of course you should continue to answer, and some people will continue to downvote! Hopefully they provide an elaboration when they do.2012-03-15