If $[x]$ represents the floor of $x$, solve the equation:
$\left[\frac{x+1}3\right]=\frac{x-1}2$
Choose the correct answer:
a) $(2,7)\cup(9,15)$
b) $(-3,2)\cup[3,4)\cup(6,14)$
c) $(-1,1]\cup[2,3)\cup(5,8)$
d) $(-5,-3)\cup(1,3]\cup[5,7)$
e) $[1,\frac32]\cup(2,4)\cup[5,7)$
f) $[0,2]\cup[4,7]\cup(9,+\infty)$
Can someone please explain how I can solve this type of equation? Thank you very much!
P.S. I'm not sure if $[x]$ is called whole part of $x$ in English, it's not my native language.