Example
we have
m(x)=2x+5
n(x)=2x+4
In this problem
m and n are linear equations
both lines are parallel
that means ------> the lines don't intersect
m(x)=n(x) ------> does not have solution
2x+5=2x+4
solve for x
2x-2x=4-5
0=-1 -----> is not true
that means -----> No solution
therefore
Yes. it is possible no value of x that makes m(x)=n(x)