\(\dfrac{x+5}{6}=\dfrac{x+5+9}{12}\\\\\dfrac{x+5}{6}=\dfrac{x+14}{12}\ \ \ \ |cross\ multiply\\\\12(x+5)=6(x+14)\\\\12\cdot x+12\cdot5=6\cdot x+6\cdot14\\\\12x+60=6x+84\ \ \ |subtract\ 6x\ from\ both\ sides\\\\6x+60=84\ \ \ \ |subtract\ 60\ from\ both\ sides\\\\6x=24\ \ \ \ |divide\ both\ sides\ by\ 6\\\\\boxed{x=4}\)
