## mathmath333 one year ago Greatest integer function

1. mathmath333

\large \color{black}{\begin{align} & \lfloor{\ \rfloor}=\normalsize \text{greatest integer function }\hspace{.33em}\\~\\ & x \in \mathbb{N} \hspace{.33em}\\~\\ & \normalsize \text{and }\hspace{.33em}\\~\\ & \lfloor{\dfrac{x}{8}\rfloor}=\lfloor{\dfrac{x}{11}\rfloor}\hspace{.33em}\\~\\ & \normalsize \text{find how many values 'x' can take. }\hspace{.33em}\\~\\ \end{align}}

2. anonymous

Can you put a restriction on $$x$$ ? think of it as $$x$$ can not be greater than some positive integer, say $$N$$

3. mathmath333

value of \large \color{black}{\begin{align} & \lfloor{\dfrac{x}{8}\rfloor}=\lfloor{\dfrac{x}{11}\rfloor}\hspace{.33em}\\~\\ \end{align}} is same for \large \color{black}{\begin{align} x< 8\hspace{.33em}\\~\\ \end{align}}

4. anonymous

good start

5. anonymous

sry $$8\le x <11$$

6. mathmath333

it doesn't satify

7. anonymous

now $$11\le x <16$$

8. anonymous

If you continue this procedure you can find that $$N$$, which I mentioned and all of solutions to the equation

9. mathmath333

for $$11\le x <16$$ it satisfies