Understanding F_spring and the Importance of the Negative Sign in -kx Formula

[etera2015]

I understand that:
F_spring = force exerted by the spring
k = spring constant = F_exerted on spring / stretch
|s| = stretch = Length_final - Length_relaxed

I'm just wondering why there's a negative sign (-) and why sometimes F_spring = k|s| [without the (-)] and when to use which.

 

[axmls]

The negative sign is left out when considering only the magnitude of the force. The negative sign is there, though, because the spring force is in the direction opposite the motion. Thus, as x gets more and more positive (pulling the spring outward), the force gets more and more negative (trying to pull the spring back in).