Question

Greatest integer function

Answer 1

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

Answer 2

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

Answer 3

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}}\)

Answer 4

good start

Answer 5

sry \(8\le x <11\)

Answer 6

it doesn't satify

Answer 7

now \(11\le x <16\)

Answer 8

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

Answer 9

for \(11\le x <16\) it satisfies