Question

What values of `c` in the equation `|2x+1|=x+c` give exactly two solutions?

Answer 1

See below.

Explanation:

This problem can be easily solved graphically.

Below we can see in blue the function `y = abs(2x+1)` and in red the function `y = x+c` for `c = 1/2` It is evident that for `c > 1/2` we have two intersections so the answer is `c gt 1/2`