f(x)=|x|，g(x)=ax+ 1

The root of solving the equation is to find the abscissa of the intersection of two functions.

Through images

If there is a positive root but no negative root, it means x0 >；; 0, and should only intersect the positive semi-axis part of f(x).

F(x) passes through the point (0, 1).

Therefore, the slope a of g(x) must be compared with the slope of y =-x.

That is, a≤- 1