quantum mechanics - Heisenberg's uncertainty principle - Planck's (reduced) constant divided by $2$ or not?

The most common form of Heisenberg's uncertainty principle I've seen online is

$$\Delta x \Delta p ~\geq~ \dfrac{\hbar}{2}.$$

However, I also regularly see

$$\Delta x \Delta p ~\geq~ \hbar.$$

Sadly, I used the latter one in a project recently and I'm afraid it's incorrect. Obviously the upper one one is true if the latter one is, but why are these two versions used instead of only one of them?