Question 825006
Solving this problem by analyzing the graphs is the easiest way I can think of...

y=|2x+1|
y=x+c

these two graphs will not intersect for any value of c < 1/2 and at c=1/2 there is only 1 intersection. So we can see that the graphs will intersect at exactly two points for any value of c > 1/2

{{{ graph( 300, 200, -3, 3, -3, 3, abs(2*x+1), x+1,x+.5,x,x-.5,x-1) }}}