The coefficient of x is simply a number. The x gives it it's meaning. So if the coefficient of x changed from 2 to 6 that would mean there would 6 x's being added to five, not 2.
For example if x=2.
instead of 5 + 2*2
(which equals 9)
it would be 5 + 6*2
(which equals 17).
The difference between the answers is 4x, as there are an additional 4x's.
