How to solve an equation involving the floor of a number? I'm looking for a solving procedure for this type of exercises.


  If $[x]$ represents the floor of $x$, solve the equation:
  
  $$\left[\frac{6x+5}8\right]=\frac{15x-7}5$$
  
  Choose the correct answer:
  
  a) {$\frac{4}5$}
  
  b) {$\frac{3}4$}
  
  c) {$\frac{7}{15}$,$\frac{4}5$} 
  
  d) {$\frac{6}{15}$} 
  
  e) {$\frac{1}{2}$,$\frac{3}4$} 
  
  f) {$\frac{1}{2}$,$\frac{4}5$} 


Can someone please explain how I can solve this equation? Thank you very much!

ps. I asked a similar question, unfortunately, the same method doesn't seem to work.
If you really want to solve it without using the fact that it's multiple-choice, notice that the fractional part of $\frac{6x+5}{8}$ is $Q=\frac{6x+5}{8}-\frac{15x-7}{5}$. Since $Q$ is a fractional part, $0 \leq Q &lt; 1$; you should be able to work backwards to find bounds on $x$. Once you have those bounds, Ilya's observation that $3x-7/5$ is an integer means there are only finitely many values of $x$ you have to worry about checking, so just try them all (or write a program to do it for you).
When you have to chose between different answers, you don't need to solve the equation, you just need to test the proposed answers.