I'm reading this as (x/3) + 7 that means the x and the 7 are separated by a plus sign. The coefficient is the number associated with any variable in the equation or expression.
Simply put in this case it is 1/3. It is not 3.
If you had something like 4x + 6y The coefficient for the x is 4 and the coefficient for the y is 6. When I was taking the stuff, they further said that the numerical coefficient was 4 for x and 6 for y. It's just a definition. Number with a variable.